I had the same problem! I used lots of lip balm, but found a few that were better than others....Blistex Complete Moisture and a product called Aquaphor, which is more like a vaseline - I used that one at night.
The good news is that I eventually got past it, but I think it took 3 or 4 months. I don't know what causes it.....and my dentist didn't have an answer either - but it will get better. Hope this helps.