Eczema Treatment Care

My child has had dry, bumpy skin since he was a child that won’t go away. I use nonallergenic detergent, and that helps slightly. We’ve moved twice, so I’m pretty sure that it’s not environmental. Other symptoms that make the dermatologist think it’s excema, are peeling, cracking skin on his palms and soles of feet when he spends any time at all in a pool. We limit baths and have used many lotions with little change. He also has a tendency to be extremely hot natured. Ten minutes of exercise and he is drenched with sweat. I can’t help to think this must be related somehow. Any advice?