There is no known medicine or product that can cure this condition or that is intended for this condition. This website has a guide from someone who claims he had EC and cured it. You can give it an attempt at best http://www.exfoliativecheilitishelp.com/
Also, has anyone tried the product stem cell therapy. It's suppose to activate stem cells in the skin that are no longer active and increase collagen production. Probably just another anti-aging marketing scheme, but could be legit.