I got really awful eczema. I do barely anything to manage it though.
I'd recommend cutting out all exogenous hormones (dairy milk eggs and meat) because they will raise your blood pressure. So will salt. I don't want to be a prude but basically any salt at all will make things worse so don't get more than you absolutely need. Plain food isnt that bad.
Diet?
Plain minute rice
Plain beans for protein (wash off the salt if you get them in a can, preferebly low sodium)
I'd reckon this could reduce symptoms a lot. I dont always follow this diet because of lack of self control but when I do it helps a lot.
Also losing weight is extremely important. If you can get below 155lbs that would be best.