When undergoing intense pain and praying for relief, what do I make of it when God does not appear to give me any relief? Did He not answer? Why wouldn’t He?

In a sense, this question is asking us to explore the mind of God. That I cannot do. As Isaiah considered, Who has understood the mind of the Lord, or instructed him as his counselor? Whom did the Lord consult to enlighten him, and who taught him the right way? Who was it that taught him knowledge, or showed him the path of understanding?—Isaiah 40:13-14.
But we do know that there are basically four answers to prayer: (1) yes, (2) no, (3) no, not yet, and (4) no, I have something better. Why God answers in any particular way is always about how He determines His greatest glory can be seen in any given situation. He knows the end from the beginning; He knows the outcome of every situation, and He sees the consequences of every action. What we can rest in is that His best will always be the best thing for us as well. And, as His children, we can rest assured that one of the markers of the Holy Spirit in our lives is looking for the “God-perspective” in all the circumstances that come our way. As Paul said so well, Those who live according to the sinful nature have their minds set on what that nature desires; but those who live in accordance with the Spirit have their minds set on what the Spirit desires. The mind of sinful man is death, but the mind controlled by the Spirit is life and peace—Paul, Romans 8:5-6. And the Bible gives us two incredible reminders as we continue on this journey with God: First, as Paul pointed out, Do not be anxious about anything, but in everything, by prayer and petition, with thanksgiving, present your requests to God. And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus—Paul, Philippians 4:6-7. Prayer is an incredible part of having a mind of life and peace, and secondly, as God famously said through the prophet Isaiah, For my thoughts are not your thoughts, neither are your ways my ways,” declares the Lord. “As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts—Isaiah 55:8-9. But as God also said, I make known the end from the beginning, from ancient times, what is still to come. I say: ‘My purpose will stand, and I will do all that I please—God speaking, Isaiah 46:10. So our purpose is to let God have His purpose performed in us, whatever that is—even if a moment is incredibly difficult or painful. Remember why we’re here: We are therefore Christ’s ambassadors, as though God were making his appeal through us—Paul, I Corinthians 5:20a. Remember also that everything we experience in this life is simply temporary; we have an eternal reality on its way that will make all these moments so worth it!