it must be very sore at the moment as its infected, poor baby!
for sensitive skin areas doctors prescribe lower doses of steriod creams.
Steriod creams for eczema are pretty tightly controlled, strength wise, a lot has changed since I was a child, and its my generation that show the side effects of skin damage.
Also my generation didnt have the moisturizers to replace lost water in skin, just the steriod.
I would continue to use the steriod creams as directed, and keep up the eczema daily treatment routine.
winter is a horrible time for face and hand skin damage, due to drying effects of wind and cold on exposed skin.
Centrol heating is another added wear on skin.
I would say USE the prescribed stuff now, as if you leave it, infection and skin damage will eventually lead to the doctor having no choice BUT to give higher strength steriods if left too long without treatment.
I am sure you have already run the gauntlet of pinning down a cause allergy wise as you have had 8 years of this battle, so are environmental allergies a factor for your child? for e.g dust mite?