Many things can cause peeling lips, among them bacterial or fungal infection, sun damage, overuse of chapstick, sexually transmitted diseases and allergies. There is no one cure that will work for everyone.
Stop the biting: you are most likely removing more skin (called the stratum corneum) than you mean to, and will regret this down the road. Try not to bite your fingernails or touch your lips either as this can spread infection. Do you have any inflammation?
Before you try any medicine or ointment, search or ask here or get on google and see what people's experiences with it are. I have started a list of treatment warnings people should be aware of. Click on my picture and go to the website on my profile, then go to Warnings.