The most likely culprits but food sensitivity is very individual ...

Food allergy and food sensitivity are very individual and so the culprit could be anything you eat or drink. However, there are foods that are thought to be more likely to play a role in eczema. These include milk and cow milk products, wheat, soy, peanuts, eggs, fish and food colourings. If none of these affect you and you feel that your diet is somehow involved persevere with your diary as this may pinpoint something you eat on a regular basis. 

Also consider discussing supplementation with a nutritionist.