Congratulations on your little one!
We use dye-free, perfume-free detergents, washes, creams everything including on the towels and washclothes (anything that touches the skin). We've also over the years learned about different allergens that have aggravated the problem.
The best OTC stuff we've found? AVEENO oatmeal products (dye-free, perfume-free), EUCERIN, Downy-free (Bounce free still had something that aggravated! but many, many people have great success with Bounce) and ALL free & clear (works better than most "free" detergents).
We were told that eczema can be aggravated by stress, environmental allergens and ingested allergens. So far that's held true...good news is he hardly ever has a problem now and we have slowly been able to reintroduce certain items (detergent) into his life w/o problem...and his eczema was horrible from the start!