In your question you have a scope of the Catholic Church, but sorta. If you don't mind, I have taken the liberty to add the perspective of the Latter-day Saints.
The King James Version of the verse you reference is: (The translation I am working with)
7 And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure.
8 For this thing I besought the Lord thrice, that it might depart from me.
9 And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me.
10 Therefore I take pleasure in infirmities, in reproaches, in necessities, in persecutions, in distresses for Christ’s sake: for when I am weak, then am I strong.
A "Thorn in the Flesh" is a weakness or weaknesses to remind us of our dependence on God. He recognizes why the thorn is there and is fine with his weakness so the Power of Christ can rest upon him.
The Lord seems to have several purposes in giving us trials: First, to test and prove us, to see if we are loyal to Him and to our beliefs. Second, to give us the opportunity to prove that we love Him more than any other thing. Third, to teach us something about ourselves and our commitment to remain true and focused on the eternal nature and possibilities of our lives, our families, and the mission of the Church.
When we understand the principle of opposition in all things, reasons for adversity and disappointment, and the blessings of trials, we can accept the daily events of our lives with greater hope and desire to endure well and to look unto Christ, that His power may rest upon us and see us happily through our mortal lives. Is it any wonder then that Paul glories in his infirmities or takes pleasure in reproaches, persecutions, and distress? These are among the vital means of growth and the development of true Godlike character.
Our Thorns in the Flesh, Elder Ray H. Wood, February 2003