Hi Josie. I used to work for a company where we focused a lot on problems originating from the GI. As you are already working on this level, that is excellent because eczema is very often related to food/intestines. The 3 primary allergens are cow's milk, hen's eggs, and wheat (whether due to gluten or to the fact that most wheat is now genetically modified into antigenic characteristics). I believe you already know this.
The 2 cents I'd like to add is that the immune system lining of your child's GI tract can also be investigated. There is lymph tissue called Peyer's patches that controls the body's reaction to foods, acting as a "customs agent" for the intestinal boundary. If damaged, then over-reactions to the foods can occur, even into adulthood. From my experience, the tests offered by Great Smokies Diagnostic Labs can provide you with further insights. NAET is an excellent choice, possibly also gentle chiropractic adjustments. There is a homeopathic remedy called Pleo Reb (aka Rebas) that is made from Peyer's patches - found it useful in situations of allergy/eczema since birth. Google search will reveal further info. Just my 2 cents...hope this helps.