There is a triad of allergy, astha and eczema that often go together (but can be individual too). My suggestion would to find a pediatric allergist who will either do a skin test or blood test (or both) for foods and environmentals on your kiddo. My son had a milk and egg allergy (when he was 6 months old) and so I eliminated both in my diet and his for six months and then retested him and he had already outgrown it(but keep in mind that both tests are not 100% accurate because though my son tested negative to milk allergy on skin test-because he still gets an allergic reaction (immediate eczema) when he drinks/eats it, he is still considered allergic to it).
For his eczema, we give our son a bath every couple of days and then right after, slather him in Eucerin or Cetaphil-something thick, oil-based and that seems to help too (he also loves "shaving" with daddy and because my DH used sensitive skin stuff with moisturizer, my son's skin is getting softer and smoother...might work for your daughter too depending on where her eczema is). Like you said, use hypoallergenic things and consider stop using fabric softener as that is a big allergic causer.
If you have a suspicion that it might be food-caused or you have a family history of allergies, keep a food diary with any allergy symptoms (for example, within minutes of having milk, my son's cheeks turn bright red and gets horrible eczema and within a few hours, he gets horrible diarrhea) for a few weeks proceeding the appt with the allergist. The skin test sounds bad, but it really isn't-I have had my son and myself tested that way-but the information you get, though inconvenient to remove it from the diet, is well worth it! If you have any other concerns or questions about allergy testing, just write me and I can give you greater details!