My doctor recommended bleach baths as well. A capful or two for entire bath.
1) You need to go to a better doctor..
2) My doctor, who is absolutely great told me that bleach baths have worked wonders for small babies with eczema (1/8 cup in a bath tub "full" of water three times a week; however, you should ask your NEW doctor about this) - after the bath, you need to use petrolatum or aquafore? to moisturize the skin
4) Do not bathe your baby too often, cleaning takes moisture away from the skin. Moisture protects the skin
3) Your baby needs to be free of dusty environments, cats, detergents, any type of odor (including Glade candles, scents, and other terrible aromas that are often marketed for households)
I have been dealing with eczema too. I have found that the only lotion I can use that works and helps his skin is St Ives lotion. Also switched to only bathing every 2 days or 3 days. It has helped a lot.
Lotion your baby up every night. With non scented eucedrin (sp.?)lotion. No products in bath, check your laundry detergent and make sure it is scent/dye free. We use elidel and something stronger that I'm not sure of name now, most importantly lotion up regularly. Find a doctor you can trust.