hello there
a friend of mine's son had very bad excema on face - she tried all sorts of things (which didnt help),but got rid of the problem after having allergy tests done (blood+skin tests) her son was found to be allergic to a bunch of foods,including dairy,soy and carrots(!)
after eliminating these foods the excema disappeared in one week!
good luck

Everyone tells you the same thing

DO NOT USE STEROID CREAM

Look at what the child is eating / drinking

A water Filter may not be the answer

What area of the world/ country do you live in

If a child is sensitive to something in the water ( like Aluminium salts used in some areas to treat water ) you will have a problem even with a filter

ELIMINATE ELIMINATE ELIMINATE

Lamb and pears are the safe things to try as start of elimination diet