I have had eczema my whole life and dermatologists are absolutely useless. I strongly recommend naturopaths.
You should only use cortisone when the patchy areas are really bad, like inflamed and rough and thick.
Don't use soap or shampoo when washing. I use organic products which made a really huge difference. I use a brand called Sukin, it has a range of shampoos and soaps and facial wash etc, all organic.
Bedding - silk is good for eczema.
When washing any of your baby's clothes/bedding etc, try and use a good washing powder. I've never found any 'organic' products, but there are special ones for babies/sensitive skin.
Also, make sure everything is Fragrance Free.
Baby wipes are also full of chemicals that create skin issues. Whenever I use them, like for changing nappies, I use a tissue dipped in water to wipe away the residue of the chemicals from the wipes.
Also diet, milk is quite lethal for eczema, try and keep it to a minimum, also orange juice or anything strongly acidic, I have found onion to be quite a trigger, even eggs. Good stuff is avocado, chickpeas, fish..
Hope any of this helps!