Firstly, It can be due to vit B deficiency. Take some vitamin B complex for some days and see if your symptoms improve.
Secondly, 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. My sincere advice would be to consult a dermatologist.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.