Hi! Your story is really touching and I'm so sorry that you are going through this!! I have had bouts with eczema my ENTIRE life (off and on) from the age of 6. I started going to a homeopath at age 7 and it has saved my life (literally). He would explain to me that the location of the eczema is telling of which organ is being contaminated and thus using your skin the rid of toxins. I had a metal cap and braces that really contaminated my body. If you have any metal Amalgams GET THEM OUT first thing. Secondly, if you can see a homeopath that does muscle testing I would HIGHLY recommend you go. My outbreaks would disappear within 2 weeks.
Here are a couple of other suggestions that I have. Watch "The Beautiful Truth" about the Gerson Therapy. It's incredible and I have used it to get rid of my eczema (when I moved 1000 miles from my trusted homeopath). It basically consists of a strict treatment of coffee enemas (to support the production of bile and support the liver during detox!) and carrot/apple juice. I also recommend ONLY drinking Alkaline Water (and using it for enemas). The important thing is to detox gently and support the function of all of your major organs (liver, spleen, intestines).
I never had much luck with Elimination Diets either but I do pay attention to foods that make me feel good energy-wise and I tend to concentrate on them. juicing has been incredible and completely changed my life.
Best of luck!!! I send you lots of light! I know how terrible it can be.