I think you have Idiopathic Endogenous Chelitis. We have been seeing such cases very frequently now. I have seen 5 cases in last 3 months. At present I can not offer you an exact explaination of the cause. But you may consider getting yourself patch tested for allergy
against toothpaste/ chewing gums/ any other special food item that you think may be causing this. Consult a dermatologist
In the mean time try Elocon cream once daily over your lips.