I have usually very unsensitive nipples. Nothing during 1st pregnancy but during my second I had intermittent nipple pain from the 2nd trimester on. It was horrible. Anything touching them when they hurt was horrible.
I went braless at home, switched to soft cotton sports bras. When they did hurt, I usually put warm compresses or rice bags and that tended to help. I could never find an answer but I just chalked it up to hormonal changes and mammary development. It went away post birth.