As a Mom to two boys with allergies and terrible eczema we have tried just about everything. Here is a list of the things that have hleped the most.
warm (not hot) bath or showers everynight, this helps remove allergins that are on their skin in the evening, it also hydrates the skin before putting on lotion. We make to put the lotion on before their skin drys, pat dry with towel no rubbing.
They are both prescribbed a steriod cream (not ointment) for itching but we try to uses in a little as possible because the side effects can include prematur aging of the skin. The lotions we put on them include petrolium jelly for really dry spot and a thick cream for the rest of the skin.
Also they are on Maitence allergie meds this has really helped allievate the itch and cut back on the eczema spots. It took trying several prescrips though some will actully dry the skin (this a problem over the counter Benadryl)
We do have carpet in our house but our allergist says it would help if we didn't.
We have seem many Dr.s about thier skin and allergies to include primary PH, derm PH and two different allergist. the routine we have developed is a result of trying what each Dr has recomended and keeping what works. Finding a good childrens Allergist has the best help. It's a lot of work but as long as we stay on top of the routine they are much more comfortable and have fewer outbrakes.
I totally agree with finding out what your son is allergic too. It can really help controll his symtoms and could help you avoid some serouis reactions. Good luck
EDIT:
Oh I forgot to meantion avoiding regular soap. It can dry the skin out. There are several brands of nonsoap cleansers. Some of the best we have found are cedaphil (can find it with the creams) and an all natural soap made by a company called Mia Bella (have to buy through a consultant) I hope I have hleped