My exfoliative cheilitis is really starting to piss me off now

No matter how much I moisturize and exfoliate, there will always be this dead layer of skin on my lips that I have to peel off or my lips will feel weird all day. Moisturizing my lips only seem to make the skin die and peel off quicker. I tried exfoliating first then moisturizing but literally the skin on my lips just die and and peel off again. Like i'll touch my lips and I can just feel the skin starting to peel off on its own. So I would pretty much have to get a tissue, rub my lips down and re moisturize. Rinse and repeat every single day. I drink so much water..too. At least a few bottles a day.