I wouldn't use talc either and I would avoid baths for a day or two.
My ds2 has suffered from excema for years. There are 3 stages of skin care:
antibiotics - fucidin prescribed - when the skin becomes infected, as your litte ones sounds to be.
steroid cream - 0.5% or 1% - for when the excema flares up - becomes red and angry.
general skin care - an aqueous cream or such like - to prevent the skin from drying out, keeping baths very cool, in fact keeping him very cool, and avoiding all soaps as they dry the skin out further. He washes in water only. I was also advised to avoid any soap other than fairy for washing his clothes and that did seem to help. Expensive, but worth it.
There are dozens of creams available - on prescription or over the counter. We worked out way through half a dozen before finding the ones that suited him best. They are more useful now that his excema is clearing up on its own (he's 3) than they were when it was bad. I never found one then that really made a difference.
If you can get to the sea this summer, the only natural thing that ever really helped our ds when he was covered in excema and a terrible state, was being dunked in the sea. It had an almost miraculous effect.
Best of luck. This is horrid to deal with, but at least he stands a chance of outgrowing it - the sooner they start, the sooner it is likely to clear.