My DD started getting eczema from about 6 weeks of age and we didn't get it completely under control until around 12 months, but I can offer you some advice that helped us:
* Make sure his clothes are predominently made from cotton
* Don't hang his clothes or bed linen up to dry outside, instead hang it inside so that the pollens etc cannot cling to it
* We used Amolin laundry liquid, its been the only one that has worked for her skin
* Have the bath water tepid, not hot or cold, and if possible only bath him every so often. Instead of rubbing his skin dry afterwards, simply pat it and then rub in cream as soon as possible. We have found that Johnsons Baby Sorbolene worked for us
* Keep a food diary of everything that you eat in a day (if breastfeeding), after a while you will notice a pattern of what flares his eczema up and makes it worse
* Don't overdress him at night when he sleeps or she will get hot and this will irritate the eczema making it real itchy
We took our DD to see a Naturopath when her eczema got really bad and he put her on an elimination diet, after about 3 months we knew what it was that flared up her eczema nd now that we know to stay away from those foods we can keep it pretty much under control. He told us that eczema derives from a digestive problem, that their gut cannot digest some foods properly, so therefore this comes out in their skin, causing the eczema. Makes sense.
My DD is intolerant to eggs, strawberries, nuts and milk protein. She can have small amounts of them (preferably cooked is better) but we just have to be careful of her intake of these foods, especially dairy.
If you have any other questions, then don't hesitate to ask.