I was reading about sesame oil the other day on a site which I believe is called http://www.youthingstrategies.com
-- and I think sesame is supposed to be helpful for eczema/psoriasis. I use it for oil pulling, and I make a combination of it and Iodine for facial cleaning/moisturizing (it also provides a mild sun-protective effect).
I am not sure if your little one would take a couple of teaspoons a day, but I know I have read that EFAs can help skin conditions, too.