Sorry to hear your lips are always dry and peeling. I would suggest a visit to a doctor or dermatologist who will ask you some questions to determine if there is any root cause to your problem such as a habit of licking or smacking lips together or use of products that may cause irritation or allergies to your lips.
This condition you have which we normally call cheilitis usually responds well to a mild steroid ointment and regular lip balm use. Occasionally oral medicines may be required if there is an underlying bacterial or fungal infection. Do see a trusted doctor or dermatologist soon to get yourself better.
Warmest regards
Dr Stephanie Ho, Dermatologist