My son had the same exact rash. It was indeed because of the formula. The doctors also gav us a prescription for cream. After I stopped breast feeding and put him on formula he started to break out. Oh my goodness, does he scratch at it? Maybe you could get an allergy test?
Im sorry, I just read the part where you said he does scratch at it :( I hope he gets relief soon!
I'm having trouble telling whether you've ruled out the possibility of Lactose allergy? I use an amazing stuff called Lacteeze that removes the lactose from milk. I also take it after I eat dairy and it digests whatever the nasty stuff is that I can't digest myself. It's safe in pregnancy, and I'd assume would also be safe for infants (though worth asking more about first). While expensive, it's worth every cent :)
My son has eczema too and I use nothing in the bath as anything like that irritates his skin and a steroid cream from the doctor. I've tried several of them though to find the right one and then I just moisturize his skin 2-3 times a day.
But I have also tried everything else. Goats milk soap, cows milk soap, aveeno, paw paw, oil, vitamin e. We've spent over $300 on creams, it's all really just trial and error. Hope this helps.