The answer to dealing with eczema might be improving gut flora and Bifidobacterium. You might find this info useful about eczema:
There are some people who have had success with vitamin D supplementation in treating their eczema symptoms.
Adding omega 3 fatty acids to the diet can also help with eczema symptoms. http://www.telegraph.co.uk/science/science-news/3337461/Omega-3-can-help-eczema.html