I recommend all of you take a look at this non-profit organization 'itsan'. Be really careful on using any steroid products! Babies would grow out of eczema WITHOUT prolonged use of steroid.
Some products may ease :
Coconut Oil
Cetaphil moisturiser
Vasline
Antihistamine - allelock a new drug better for eczema but only available in Japan and China
Bleach Bath to kill bacteria on skin (1-2 times a week) (concentration 0.005% ~ to swimming pool)
ice pack may alleviate itch
Fish oil, probiotics, supply may help
Dead sea salt bath
Antibiotics to treat serious infection
Telfa AMD/Bactigras can prevent inflection if oozing occurs (running out liquid)
wet wrap on serious case (search it for more info)
Be careful on using any steroid products!
There is no magic formula for eczema now. Good luck!