From the years that i've had this problem, one thing i've learnt is that peeling off the excess skin causes more irritation, and fresh wounds. Any skin specialist would tell you that peeling is not the solution. I've learnt to go about this problem by cutting off the excess dead cells using a handy surgical scissor. Secondly, unlike what one might think, licking the lips eventually increases the dryness factor, perpetuating further damage. As a matter of fact, many chronic lip lickers have developed this problem from that very act. This is just my tidbit, hope it might be of use.