stillbattling
At times I had what seemed like peeling lips. But it was actually some very thin things attached to my lip.
You might try rubbing oil or neem seed oil on your lips, then wipe off after a little while. Some might come off when you wipe; you might be able to peel the rest off.
I have candida and various parasites, so really don't have any idea what I had.
This cured my problem.