I live in the UK so this might not be the case in the US but over here Medical Doctors know nothing at all about nutrition because they weren't taught it. You can't expect western doctors with their microscopic approach to advocate a holistic/whole body approach.
I've had mild eczema since birth. It got a lot worse age 20. On the plus side the doctors advised:
1) no hot baths
2) no soaps
3) pat dry instead of rubbing
4) did an allergy test (food wasn't invloved)
5) advised about dust mites
On the downside I took antihistamines for years and hydrocortisone.
I've been on a gluten free diet for two years and avoided dairy products. Other things that have helped include:
accupuncture & Traditional Chinese Medicine
chi gong & tai chi
shankaprakshalana (yogic bowel cleanse)
replacing carpet in room with wooden floor
yoga - particularly pranayama