I have exfoliative cheilitis (peeling lips) and the only lip balm that soothes my lips and helps stop the peeling is called "Daily Conditioning Treatment (DCT)" by Blistex.
It's often available at stores with pharmacies such as Rite Aid or CVS. Sometimes you can find it at grocery stores. You can also order it on Amazon.
The ingredients are pretty good including aloe, vitamins A and E, cocoa butter, and camphor, etc.
Notes:
*The lip balm does contain sunscreen and I personally try to avoid lip balms that contain sunscreen, but so far this is the only lip balm that works for me.
*Also, for me, using this lip balm is a good short term solution while I try to manage the underlying causes of exfoliative cheilitis such as overgrowth of Candida yeast.
All the best to all of you out there that are dealing with exfoliative cheilitis! Hang in there!