It seems that you are having chelitis.
There are many causes.
It may be solar, vitamin deficiencies like riboflavin
, drug induces like retinoidss, anaemia
, internal diseases, irritation,allergic, stress
You should be thoroughly examined and investigated to find out perfect cause.
Treat the cause.
Avoidance of sun exposure, irritant like cosmetics, toothpaste or other chemical should be done.
Take vitamins containing riboflavin and B 12, minerals like Zinc.
Apply moisturiser like liquid parrafin,lactic acid..etc
Do not rupture the skin of lip.
Have healthy food and proper sleep.
You consult dermatologist
for perfect diagnosis and treatment.
I hope you might be satisfied with my answer.
Dr. Ilyas patel MD