All 3 of my boys had terrible eczema and asthma. Not only were they on steroid creams we gave them benadryl every night so they could sleep. It helped them sleep but, like you, I didn't like the idea of them being on benadryl long-term.
This is what I learned from my experience. It is vitally important that you find out what is triggering your baby's eczema. It could be a food, pollen, pets, preservatives, or other chemicals. Some of the ingredients in every day things like laundry detergent, body wash, and even cleaning products were extremely irritating to my boys' skin & respiratory systems. When we stopped using things with bleach, ammonia, or formaldehyde, my boys' skin cleared up so much!!!!!!! They don't need Benadryl to help them sleep anymore because they don't itch! I'd be happy to give you all of the info about the things that we do use. :)
D.