I had a similar experience with DD, GP also diagnosed it as Excema, but nothing prescribed worked at all
Thankfully I was pointed in the right direction by a good friend who works in alternative health, specialising in babies & Children
turned out my own DDs problem was actually intolerance to food additives, taken in via my breast milk, once I'd cut all those out of my diet, her skin cleared up very quickly :) -
she is 8 & still has the problem now, but so long as we keep her diet additive free, her skin is beautiful - its something the NHS now take seriously, as at a recent dietician appointment I was impressed to be taken seriously, & they even had print outs of all the main culprit additives
with DD its Azo Dyes, Benzoate preservatives & MSG - sweeteners also effect her, but usually her stomach.....realised afterwards that DDs flare ups coincided with my hormonal cravings for cheap jelly sweeys 
There is also a natural cream - Zambesia Botanicus - AKA Sausage Tree cream, you can buy it in most health stores, it really helped with DDs skin & a friend in the US stocks up on it for her own DD who has true excema - this is a mild natural steroid, but not anything like as much of a worry as the prescribed stuff, but worked better for us & friends DD
We also found that Epsom Salt bath, with added oats & lavender oil helped sooth both her skin & her frayed nerves & helped her sleep too
Also not bathing too much - we were advised once a week or risk drying her skin & making it worse - this did help too
I'm curious - has he had antibiotics?? - I ask as DDs problems got FAR worse after anti B's for Bronchiolitis & later worse still after pneumonia - & more so after another chest infection - & I've seen another thread on here where others had noticed a link too
I hope you find some relief for him soon poor mite, I bet your nerves are frayed with it too :(