Any chance you've got a yeast infection? From the way you were describing it, that's kind of what it sounds like to me. Vaginal yeast infections are pretty common during pregnancy, and it can be spread to your nipples. Usually this only happens if you are nursing and your baby has thrush, but I have had it once when I wasn't nursing. If you think that is a possibility, talk to you doctor/midwife about using an anti-fungal cream on your nipples.
Hope you get some relief one way or another!