A lot of you posted great advice and questions so here's a summary of that info.
The pinching occurs at the end of feeding when my breasts are not full. When my daughter comes off there is a slight crease on the side but the nipples is still pretty round. My LC said that it looked ok when I brought this up.
I did have thrush a couple of weeks ago so I just finished a round of diflucan. The aching and pinching is different from the pain I experienced with the thrush so I think it's more of a latch problem.
The pain is getting better. I no longer have intense pain with the initial latch, it's just the end of the nursing period that really hurts. I do think that comfort sucking is when it occurs, which she has been wanting to do a lot more this last week (she had a bladder infection), so she has spent a lot of time just nursing. By the end of the day I'm really sore and aching but in the morning it's not that bad.