You are suffering from lip dermatitis. The symptoms you mentioned, such as cracked lips, white patches, and skin peeling off, are the typical signs of lip dermatitis. Lip dermatitis can be the result of dry weather, periodically licking the lips, or the use of severe lip products. Use a gentle lip balm and refrain from licking the lips. Proper nutrition and protection from damaging UV radiation should be observed to prevent harmful effects on the lips. If the discomfort persists, visit a dermatologist.