I'd definitely get him to the doctor.There could be all sorts of reasons for his symptoms.
However, if it is diagnosed as eczma, there might be something you could try.When the girls were little, they both suffered very badly from eczma and I was extremely wary of steroid creams. Eventually, after being prescribed various ineffective aqueous-type creams, a doctor prescribed a cream called "Unguentum Merck". Nothing nasty in it at all, but not regularly prescribed because it was relatively expensive.I used this every day and used Oilatum in their bath instead of soap or baby bath products. Within a month of using it, both were free from eczma and have not suffered since. Many friends have also used it when nothing else seemed to work - always with good results.I don't know if it is still available, but it might be worth looking for.