food allergies are really just trial and error. before 1 years of age allergy tests are pretty bad, and even afterwards, you generally only want to test if you suspect a specific allergy - there's often a false positive result, and it will tell you that your child may be allergic to something that they may not actually be allergic to
if there's a specific allergy you're worried about that is in the immediate family, like say peanut butter, you could try putting a smear on your child's skin to see if they have a reaction from that first
and for eczema, typically it flares up when teething or with viruses (and in more situations). it's not something you can really expect to resolve, more of a wax and waning situation. if it's there pretty often you may want to use steroid creams, i'm assuming that's what you mean by prescribed creams. in general, you should apply moisturizer at least twice daily. you want to avoid soap and full baths as much as possible, maybe just 2-3 times per week would be enough. a quick rinse is fine, don't dry off completely and then make sure to apply the moisturizer cream on top of moist skin to kind of lock the moisture in.
it's important to understand that it's really an underlying defect in his skin that makes it less effective as a barrier, which is why it's something that probably won't go away for a while. he may kind of outgrow it eventually, but like i said, it will come and go for a while. also odds are he got it from one of you guys, especially if there's seasonal allergies, asthma, or eczema in the family
