What is the full context for Jeremiah 17:9? With a verse like that, how is it possible to trust what our hearts say about anything or do anything that we “feel” is right?

Jeremiah 17:9 says: The heart is deceitful above all things and beyond cure. Who can understand it?—Jeremiah 17:9. But it sits in the middle of an incredible context—a single verse from the prophet within comments from God Himself. The chapter opens with God declaring judgment on the nation of Judah for their sin, and He does so in incredibly graphic language: Judah’s sin is engraved with an iron tool, inscribed with a flint point, on the tablets of their hearts and on the horns of their altars. Even their children remember their altars and Asherah poles beside the spreading trees and on the high hills. My mountain in the land and your wealth and all your treasures I will give away as plunder, together with your high places, because of sin throughout your country. Through your own fault you will lose the inheritance I gave you. I will enslave you to your enemies in a land you do not know, for you have kindled my anger, and it will burn forever”—God speaking, Jeremiah 17:1-4. God starts out by saying, by means of the imagery of an iron engraving tool, that Judah’s sin is indelible—imprinted on their hearts. If in fact their sins or so inscribed, then God’s judgment for those sins is inescapable. How far have they moved from God’s intentions for their nation; in fact, their worship was now a profane blasphemy of foreign gods. It was David who had originally said, You do not delight in sacrifice, or I would bring it; you do not take pleasure in burnt offerings. The sacrifices of God are a broken spirit; a broken and contrite heart, O God, you will not despise—David, Psalm 51:16-17. It was in their hearts that the most profound idolatry had been performed and, because of the extent to which they had so willingly turned their backs on God, God in turn was going to turn them over to enemies from foreign countries, reflecting His anger at their sins. It is out of that anger, and as a commentary on sinners in general, that He then continues in verse 5, where God says: Cursed are the one who trusts in man, who depends on flesh for his strength and whose heart turns away from the Lord. He will be like a bush in the wastelands; he will not see prosperity when it comes. He will dwell in the parched places of the desert, in a salt land where no one lives—God speaking, Jeremiah 17:5-6. The message is clear; God is declaring what as Jesus Himself would say centuries later, [A]part from Me you can do nothing—Jesus Christ, John 15:5b. A person trusting only in himself—his own strengths, his own abilities, his own wisdom—cannot thrive. It is an impossibility. The imagery is that of a native plant of the desert lands of the Middle East—the dwarf juniper. This plant’s leaves are not refreshed by rain whenever it comes, so it remains both stunted—under-developed—and starved. But then comes the wonderful contrast of the life lived in the pleasure of God: But blessed are the man who trusts in the Lord, whose confidence is in him. He will be like a tree planted by the water that sends out its roots by the stream. It does not fear when heat comes; its leaves are always green. It has no worries in a year of drought and never fails to bear fruit”—God speaking, Jeremiah 17:7-8. Trusting in the Lord—that’s where the blessing is. Because of that, no circumstances need be feared. In fact, abundance is promised, and growth and fruitfulness are assured. Sounds good so far.
But then comes Jeremiah’s momentary cry of desperation, as he realizes the core issue: The heart is deceitful above all things and beyond cure. Who can understand it?—Jeremiah 17:9. In other words, he is overcome by the innate, inherent depravity and wickedness of the human heart—which in this case symbolizes the total human inner being, including reason, action, and will. It is truly, on its own, “beyond cure.” Even the owner is stunned by its confounding, deceiving wickedness. What can be done? Jeremiah literally aches for an answer.
The answer comes from God Himself: I the Lord search the heart and examine the mind, to reward a man according to his conduct, according to what his deeds deserve—God speaking, Jeremiah 17:10. God reassures Jeremiah that the Lord knows the truth about the heart, and He will deal with every heart perfectly, according to our deeds. Jeremiah can rest in that.
Now, as Christians, we can know that a couple of things have happened to us—all by the work of God through Jesus Christ: (1) Our sins are completely forgiven and removed from God’s own sight and memory, and (2) We are filled with a deposit of Jesus Himself in our lives—the Holy Spirit. All that we need in Christ has been done; Paul said it this way in some of the most amazing words found in Scripture: So then, just as you received Christ Jesus as Lord, continue to live in him, rooted and built up in him, strengthened in the faith as you were taught, and overflowing with thankfulness. . . . For in Christ all the fullness of the Deity lives in bodily form, and you have been given fullness in Christ, who is the head over every power and authority. In him you were also circumcised, in the putting off of the sinful nature, not with a circumcision done by the hands of men but with the circumcision done by Christ, having been buried with him in baptism and raised with him through your faith in the power of God, who raised him from the dead. When you were dead in your sins and in the uncircumcision of your sinful nature, God made you alive with Christ. He forgave us all our sins, having canceled the written code, with its regulations, that was against us and that stood opposed to us; he took it away, nailing it to the cross. And having disarmed the powers and authorities, he made a public spectacle of them, triumphing over them by the cross—Paul, Colossians 2:6-7, 9-15. Those words are huge because it means that it is all about God, and a work He is doing, that we can place our reliance on. We don’t have to wonder; we don’t have to check our feelings. It’s happening by His design, His plan and His grace—regardless of us. We can trust our hearts because of Who’s reworking our hearts. We have the Holy Spirit in us, guiding us, directing us, correcting us as we continue to be remade in the image of Christ Himself. Paul explained this work as an ongoing process every day of our lives, being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus—Paul, Philippians 1:6. One way we see that is when we experience, in Paul’s words, “godly sorrow.” As he said to the church at Corinth, Godly sorrow brings repentance that leads to salvation and leaves no regret, but worldly sorrow brings death. See what this godly sorrow has produced in you: what earnestness, what eagerness to clear yourselves, what indignation, what alarm, what longing, what concern, what readiness to see justice done—Paul, II Corinthians 7:10-11a. It is one of the wonderful ways that the Spirit gives evidence to us about what has occurred between us and God through Jesus Christ; as Paul said, The Spirit himself testifies with our spirit that we are God’s children—Paul, Romans 8:16. And, as Christians, we can know even more: First, we can know that the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express. And he who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for the saints in accordance with God’s will—Paul, Romans 8:26-27. And second, we can know that he [Jesus] is able to save completely those who come to God through him, because he always lives to intercede for them—Hebrews 7:25. Bottom line: We can trust what is occurring in our hearts and, in fact, the directions of our hearts, by what God—based on the completely sufficient work of Jesus Christ—is doing in our hearts. Like has been said, it’s all about Him! And eventually—and ironically—we have a future to look forward to that Jeremiah described in the future that, by God’s grace, His people could still one day look forward to: “The time is coming,” declares the Lord, “when I will make a new covenant with the house of Israel and with the house of Judah. It will not be like the covenant I made with their forefathers when I took them by the hand to lead them out of Egypt, because they broke my covenant, though I was a husband to them,” declares the Lord. “This is the covenant I will make with the house of Israel after that time,” declares the Lord. “I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people. No long will a man teach his neighbor, or a man his brother, saying, ‘Know the Lord,’ because they will all know me, from the least of them to the greatest,” declares the Lord. “For I will forgive their wickedness and will remember their sins no more—Jeremiah 31:31-34. Did you hear that? Those same hearts so helplessly engraved by sin will now—and forevermore—be engraved with the law of God. Wow! And this is also why we study the Scriptures, God’s word of truth, so that we can know what God says, and let our doubts and concerns be settled by His declarations. Praise His name!