You might be suffering from Cheilitis. There are different causes for this condition. Lip licking, using cosmetics, using a new toothpaste and deficiencies of certain vitamins can also flare this condition.
Next Steps
Consult a dermatologist.
Health Tips
Avoid lip licking, avoid using cosmetics ( especially matte long stay lipsticks) , use a fragrance-free, non-tinted lip balm.