Is it dairy? Or something else? Does he have multiple allergies? Is it a food allergy at all? 
It certainly is tough to know whether LO's eczema is related to allergies, be it food or otherwise. A lot of eczema cases are though.
I find that I have to keep DS's skin well hydrated - meaning LOTS of cream, all the time. If his skin is dry he tends to get really irritated by it and scratches until he bleeds. I also have to use steroid cream on occasion to get his skin back under control, as he can have major outbreaks. But def the key to managing his skin is to slather him with cream. I use a variety depending on the situation; Aveeno (the sensitive one with oats) is good, aqueous cream (non petroleum base), Weleda eczema cream.
Until you can get him tested perhaps you may want to try an elimination diet? How strict are you with regards to keeping of diary? I was really surprised to find dairy in a lot of foods that I didn't even think about. I had to read every single label fastidiously.
HTH.
Lien.