My 2month old is diagnosed with the same problem and doc gave Bioderma Preventive for atopic skin. It relieves the redness and itch but when you stop using it, it comes again. I have searched the web and found out that there is no exact cure for this. And I found a herbalist living in the eastern part of Turkey, who has been dealing with skin problems almost for 15 years. He prepares organic creams with essential oils and herbs. He sent me a cream and eczema disappeared! I have seen other pics of babies healing in a week. Unfortunately, he could not afford to get a patent and the medical firms said he has to give money for the rights of the cream. And he has to wait for 10 years to get it. So, he helps individuals who can reach him. (it was quite difficult even for me!)
I hope we will find a medical firm to help him produce his creams.
What I want to say is, it is actually possible to cure eczema with natural oils.