It seems like that you are having cheilitis. Since it is chronic, so it can be due to atopic dermatitis or eczema("Atopic" refers to a group of diseases where there is often an inherited tendency to develop other allergic conditions, such as asthma and hay fever). Cheilitis(Inflammation of the skin on and around the lips)is often seen in atopic dermatitis. Diagnosed by blood test like RAST. Treatment is by topical steroids or oral therapy of corticosteroids in severe cases. Topical creams like tacrolimus ointment (Protopic) and pimecrolimus cream (Elidel) are also useful.
I sincerely hope that helps. Take care and regards.
In addition to what was already said, I would suggest taking extra riboflavin. It is water soluble. I have the same problem and for the reason the doctor already suggested. But, when I started taking the extra riboflavin (vitamin B2) as suggested by my neurologist as a migraine preventative, the extreme skin peeling on my lips calmed down considerably.
Also, get your B12 level checked. It's one of the vitamin levels that can be checked. You can still supplement it and all, but you need to find out if it's low or not. My doctor checked mine and said it was fine. She explained that the levels are stored in the liver and only need to be checked about every three years, unless there is a problem.
Also, consider taking a B complex formula. Most of the B vitamins are water soluble. I started taking the highest amount available through Trader Joe's, which is inexpensive to hopefully take care of the other B vitamins. It seems that even though I've had problems taking B complex in the past that their formula doesn't bother me.
I also take one 800 mcg folic acid capsule each day. You don't need massive volumes of this one, but it is a necessary nutrient and will help the skin in addition to all else that it does.
I actually learned about this on this site.