My mom went through this with my brother in the 70s and 80s and the only thing that would work was Avon skin softener, the kind in the little jar or pot. It didn't help my daughter though. She finally figured out he was allergic to soaps and perfumes of any kind. He can ONLY use original scent Tide.
My sister went through this with my niece and nephew. They were both allergic to milk products. He outgrew it by the time he was 3, she took until she was 10.
My daughter had it so badly on her bottom and hips that we went to three pediatricians a naturapath, a chiropracter, and a dermatologist. Not to mention a lot of online research. No medicines, creams, prescriptions,baths, diaper brands, detergent, etc. worked. We took her off of milk because we ran out and her brother had goat milk and she liked it so we kept buying it for her. Her skin cleared up but we didn't think much of it since it was summer and she was naked all the time. I gave her a bottle of milk one day from McDonalds on a road trip to grandma's. 3 hours later her whole butt was broken out. We have not let her have cow milk since and she is ezema free.
All of these issues in my family were resolved by taking away milk except for my brother who still drank milk and still had eczema. He was stubborn!
I would cut any and all cow dairy from his diet. If you are formula feeding, then he needs to go on dairy free, not just lactose free because it is the milk protein that is probably doing it. We had to use Alimentum for them. I know others use Nutramingen, I honestly dont' know the difference.
If you are breastfeeding, then get some formula while you get all the dairy out of your system. I couldn't have any while I was pregnant or breastfeeing because they reacted so strongly to it!!
I hope that helps your little guy. It really did my family; there is a lot of research out there that connects milk and skin conditions. Even vets are talking about skin conditions in dogs and cats from food allergies because its so connected.
I hope this helps you. it really is where I would start if I were you.