Just as a note, my family (including myself) has eczema. Ours are related to food allergies. My GP (an internist) and a dermatologist have both said it's impossible, but our eczema flares up when we ingest an allergen (eg, if I have something processed with nuts or if my son has more than one small glass of milk a day). Once it originates, there's no stopping it except to smother it in vaseline or eucerin, cortaid, benadryl, whatever cocktail happens to work at the time, and stay cool, as unclothed as possible, and stay out of the sun. You may want to test this for yourself with your son and see if eliminating common food allergens (one at a time) has any positive effect. Mine usually takes two weeks minimum to heal tho once it's originated so pinpointing a food allergy will be more difficult with eczema than anaphylaxis if that's the issue.
FYI, we also use Neutrogena as long as it doesn't contain any nut oil(s). Good luck!