All three of my kids have had eczema... luckily 2 of them out grew it quite early - the youngest at 5 is still dealing with small patches. Elidel or Elidol... something like that was the miracle drug that we started using with #2 and #3. The eczema patches cleared up in just a few days. It was a salve. We also used a ton of aquaphor.
Just so you are aware... there is a high likelihood that a child with eczema will go on to get allergies, especially environmental allergies (dust/pollen/molds/etc). I'd advise that you start taking the typical environmental allergy precautions now to either lessen impact on the child or just so you are used to them.
One thing that is hard on the child is if they have a room full of stuffed animals... having to get rid of them. Do simple things like store all but one or two special ones anywhere but in the child's room.
Put dust barriers on their pillows/beds. If they are used to that feel they won't mind... my son HATES his pillow with the dust barrier just because it is different than what he was used to.
No pets in the bedroom
bathe at night (to remove pollen - especially this time of year)
Use a hepa air filter in the bedroom
if you are remodeling anyway... don't put carpeting in the bedroom. We have carpeting and thus have to do a dust mite treatment every 4-6 months. It is a pain, but hardwood or tile for all the bedrooms just isn't in the budget. The doctor asks every single time... "Have you removed the carpet yet?"
If you are lucky you won't have a child with allergies... but if you do you are prepared. Unfortunately all three of mine have allergies - the oldest has mild allergies that don't need to be treated except for using an OTC antihistamine. The middle one is highly allergic to just about everything in the environmental panel. There are probably 100 things they test for in that panel and he didn't react to SEVEN of them. He is doing immunotherapy and is greatly improved. The youngest is going in next month to the ped to have a blood draw to start allergy testing.