Many years ago I had such bad eczema - 3 types, I didn't know there were 3 types - that I thought I would never work again. I couldn't drive, could barely sleep, walked with a stick, and was in constant pain. I had to have a bed frame, such as burns patients have, to keep sheets off my legs, and wearing trousers was too painful so I was wearing shorts in the winter. I was given various creams, but none of them make the eczema go away. People who saw my legs and face assumed I had been in a fire.   

Doctors sent me for tests, found nothing, gave up, and said I'd had to live with it.

I bought a book on food allergies. It said to find out what you are allergic to, drink only water and eat only potatoes for a week. It listed the common culprits, which included dairy and onions, and said to reintroduce foods one by one. When you get a reaction, you know you have found the culprit. I found my culprits (onions, dairy, leeks, peanuts) and stopped eating them. Within a fortnight I put the walking stick away. It took 6 months for all my scars to heal but all this was 15 years ago and my eczema has never returned because I have been strict with my diet.

Hope this helps. It's worth a try.