My son had these exact same symptoms. His ezcema started in the folds behind his knees and eventually became like sunburn all over his body. He was 3 years old at the time.
We eventually discovered that it was the water where we lived. Luckily, we only lived there for 6 months. His eczema cleared up a few weeks after moving.
In the meantime, his symptoms were totally alleviated by olive leaf extract. I gave him some in his juice twice a day and also mixed some in burt's bees lotion and applied it topically twice a day. This made the eczema totally disappear, but when I tried to wean him off, he would start getting itchy again, and would get an all-body rash within a day or two. The brand I used was Gaia herbs, in gel-caps (because it was alcohol-free); I would snip the gel and squeese the extract out. I purchased it at Whole Foods Market.
The key is to find out what is the cause. Different kids react to different things. Many people will tell you to eliminate wheat and dairy from the diet. I can only tell you that, in our case, it was the water. So if you suspect the water, try washing only in distilled water and (of course) do not drink or even cook with tap/flourinated water, and do not use flourinated toothpaste.
Just a note that our doctor prescribed Ellidel. I threw it away. It works by supressing the body's t-cells (immune system). It only temporarily relieves symptoms and has been shown to cause cancer, especially in small children. I would not reccommend any medication given by a doctor. Perhaps, if your friend believes in doctors, an allergist would be the one to see, to determine what her son is allergic to, then avoid that substance.