My fingers used to do the same thing comercial fishing up north but that was due to wearing gloves soaked in the salt water.I have never had this happen from egg cures but I have had them dry up after a day but never peel or crack.

I used to smear my hands with bag balm and wear cotton liners to bed to help my hands along and actually if I did it every night it would actually go away but I am talking months of abuse not a week end of fishing

I would almost say that you are alergic to procure and might want to try a diferant cure.