It seems that you may be having chelitis.
There is dryness and peeling of labial skin.
There may be some cause.
Sun rays,irritants,allergens,cosmetics,lipsticks,dental cream,drugs,stress,vitamin and nutritial deficiencies,anaemia,immunodeficiencies,some genetic diseases..etc can cause chelitis.
Avoid soap,cosmetics,sun exposure...
Have blood test
to rule out systemic diseases.
Apply moisturising cream.
Take folic acid
and vitamin E
A void worries.
Have good sleep and healthy food.
However, you consult dermatologist
Dr. Ilyas Patel MD