Feel for you but don't ave surgery. I had ec for over 30 years. I had I biopsy last year which showed my lip problems were the result of eczma. My lips are in a good condition now ( only slightly peeling ) but after the biopsy the peeling continued when the wound healed. I assume the same thing could happen after surgery. Have a biopsy with a dermatologist to see if that will show the cause of the peeeling rather than resorting to surgery.
If the cause is diagnosed you can find suitable creams to treat lips.