The answer to dealing with eczema might be improving gut flora and Bifidobacterium. You might find this info useful about eczema:
http://www.ncbi.nlm.nih.gov/pubmed/16601353
http://www.marksdailyapple.com/whats-up-with-your-gut-beneficial-bacteria-and-good-digestive-health/
There are some people who have had success with vitamin D supplementation in treating their eczema symptoms.
http://www.fitnesstipsforlife.com/vitamin-d-as-an-eczema-cure.html
http://www.news-medical.net/news/2008/10/06/41864.aspx
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