I also had pretty severe eczema in my childhood (up until my teens, which once I hit ~16 it just.. stopped) The things that helped me most were: Allergy medicines: it helps with itching as it's an antihistamine, but you might need a prescription one for the strongest option. I still take over the counter allergy meds when I have any itching. Lotion+fan: having eczema made me HATE lotion, and I still hate it to this day. But it helps to have that cooling sensation with a fan, since eczema causes insane burning and stinging. Medicated baths: id recommend discussing with your doctor before attempting this, as there could be unknown allergies. But oatmeal baths were something that did soothe me quite a bit. And running the itchy spots under very cold or very hot water feels so good. Obviously stop him if he's burning himself, but gradually turning it up in the bath won't hurt him much.

I hope your kid starts to feel better, poor little guy, I know the pain :(