You are right Paul was conceited and he knew that was a personal flaw he had. It shows up over and over through out scripture that he thought more of himself than he should but then he would repent for a while but then go right back into being conceited again. He never seemed to be able to let God heal him of that one flaw and let it go.
The truth is, God still used Paul even though he was conceited and that thorn was a constant reminder to do better. Pain is a real attention getter. God knows us better than we know ourselves and He is very much involved in our learning process of becoming better people.