Most agree the order in which Paul wrote his epistles are as follows: 1st and 2nd Thessalonians, 1st and 2nd Corinthians, Galatians, Romans, Ephesians, Philippians, Colossians, Philemon, 1st Timothy, Titus, and 2nd Timothy. To the astute student it is clear there is a progressive revelation in these thirteen letters. For example, in his earlier writing he looks for the immediate (at hand) return of our Lord, but toward the end of his life and ministry he stresses His imminent (expectant) coming.
This principle holds true as to healing also. At the outset of his ministry, Paul saw, and was an instrument, in many being miraculously healed. But toward his later years, there is a noticeable absence of such healings. In his last letters (prison epistles), we read of some of the Apostle's closest friends and companions being sick, but strangely, he would not heal them. For example, Epaphroditus, for of the work of Christ, was nigh unto death; Trophimus was left sick by Paul at Miletum; and his beloved son in the faith, Timothy, had constant stomach problems. Paul didn't use his gift of healing on any of them.
In the first case, God showed mercy upon the sick one by raising him up; in the second, we are not told the outcome, simply that a precious brother was left behind sick; and in the third situation, the young man was advised to regularly take "a little wine", for his oft infirmities. Interestingly, Paul's constant companion in his travels was a medical doctor, Doctor Luke. Healing in the early days of Christianity was not just a compassionate thing, but a confirmation. That is, attesting to one's apostolic authority. As the authoritative Word was completed, the apostolic authoritative signs and wonders ceased.
God still heals miraculously, if He so chooses; but generally, in our day, He uses means. The rule seems to be: in the Old Testament and coming into the New, God healed directly, using means sparsely; but toward the close and completion of the New Testament, the reverse is true. Today there is no cut-and-dried way as to healing in a saint's life. God has a sovereign plan for each life, and deals with us accordingly. It is well to remember that those who are healed miraculously or by use of means, still ultimately die. Remember Hezekiah! God healed him, but only for a fifteen year period. Then he died.
If we were as concerned with the healing of our souls as we are our bodies, what spiritually robust Christians we'd have.