It is well known that cracked and peeling skin is oftentimes a result of a food allergy or food intolerance.
When my daughter was 3 months old, we discovered she had an allergy to cow milk simply because the skin around her neck started to peel. All on its own. She hadn't been out in the sun, nor had she gotten into anything that would have "burned" her. It was ugly, red, and hurt. I quit feeding her formula (she was breast fed; I was unable to breast feed) with cow milk in it, and all of her peeling skin went away--almost overnight. She's never had an issue since. We kept her off cow's milk until she was 1.5 years old. Now she is 11 years old and has started having issues again, so we've taken her off cow's milk again. Even though she seemed to have "grown" out of her cow milk allergy, it's always possible for her to get it again--and keep it (both her mom and dad are allergic to casein).
I would RUN to a Naturopathic Doctor and have your son tested for cow milk allergy (done with a saliva test--tests for milk, egg, soy, gluten) and then, while you're there, I'd also get a food intolerance test taken (doesn't cost a lot).
Allopathic doctors are NOT trained at all in food and nutrition and how food issues affect (adversely) the body. They will continue to tell you what to put on/use to "control" the sores/peeling, but they will not be able to get to the root of the problem, or the cause, and help you get rid of the what's causing his sores/pain. I know; 40 years of missed diagnoses of food allergies and food intolerances means 4 years of me still trying to get my body healthy. I've been working with alternative care/health doctors. They are the ones helping me get better, not the allopathic doctors.
If he were my son, I would do everything in my power to figure out what is causing the peeling/sores, then eliminate that problem from his diet, if necessary.
Good luck.