I would double check with the Dr to make sure it is ezcema and not psoriasis, which has differnt types of treatments for it.
My daughter has psoriasis on her face, because of how close it is to her eye we cant use many treatments, but we have been able to use some. As far as OTC, I have found the California Baby products to be the best bet. They are more expensive but they work wonders on sensitive skin. All the baby boutiques in the Sac area carries them, as well as Whole Foods. Target carries some items but not their rich creams. I find their Calendula Cream works the best.
I do not like baby aquaphor because its main ingredient is mineral oil. Considering no matter what you will have to be doing multiple times a day application of anything you use, I want to use something safer for my baby. I think it works well for a quick rash or a diaper rash, but not long term use.