B.R.
Our daughter had severe eczema as an infant, and our ped. ordered allergy tests, which revealed a life-threatening peanut allergy at 15 months, fortunately before we fed her peanut butter. (she was probably sensitized in utero or while breastfeeding). Definitely see an allergist and get both a skin prick test and a blood test, called the RAST test, which measures allergen-specific IgE antibody levels.
You might be able to control the eczema by identifying underlying allergens. We were told to give her frequent baths, and to use eucerin cream (not the lotion, but the Crisco-like cream), as well as a prescription steroid cream. Before you get a prescription cream, you can try something like cortizone 10 cream. Also, use cetaphil to wash with, not soap. Meijer has a cheaper generic version of cetaphil. We found that wearing all cotton clothes helps, and we switched from Tide to Arm&Hammer free detergent. Tide is the harshest detergent out there.
There's also prescription elidel and protopic that you can try, but we don't use those anymore.
Our daughter is 6 now, and still gets some patches of eczema now and then, but it's much less severe than when she was a baby. Don't know if it will go away completely, just have to wait and see.
Also--ask your doctor about giving him a probiotic supplement. Some formulas now have probiotics (Nestle Good Start Natural Cultures, and I think Similac is making a probiotic version as well). Probiotics have been shown to help mitigate eczema--and they're totally safe.