I had this same miserable problem for years. Exfoliative cheilitis. I've been cured completely by Epiceram, a prescription ointment. I still have to apply it multiple times per day, but as long as this medicine exists, I'll never have EC again.
BLISTEX is a scam. Every single thread about lip problems has these same posts claiming that Blistex is a miracle cure for whatever the problem is. It is not. I fell for the scam two years ago. I bought blistex 3 years ago to try to cure my EC, and it did nothing. Blistex may help for normal chapped lips, but if you have a "medical problem" like exfoliative cheilitis, it not the answer.