I know you've gotten lots of suggestions on this topic. Our DS has eczema. Not as much as he used to but he still gets it. His is not due to milk or egg allergy. It is quite common for bi-racial and Black American children to have it. DS is bi-racial. We took him to the pediatrician and he gave him this cream type stuff that didn't work. I was disappointed. I went on one of my message board groups for parents who have adopted bi-racial or transracial children and asked the same question. The solution for us was Eucerin Calming Creme. It worked like a charm and we try to use it regularly to keep DS's eczema from coming back. I have met other parents who like me swear by it. The stuff is amazing. You can buy it at Target,
Walmart, drugstore or other major discount retailer. It's not super cheap. I think I pay about $10 for the largest squeeze tube they make but it lasts awhile for us.
Hope this helps!