Kazack,
I was diagnosed for many food intolerances using kinesiology. I have since read that success with this technique is heavily dependent on the skill of the practitioner, but I have to say it was very successful in my case. It does look a bit like magic as Pupuce describes, but I can only conclude that there are more things in the world than we currently understand. The doctor warned me that he could not guarantee success, but aimed to give an approximate picture of what I was reacting to, and that proved to be the case. He successfully diagnosed and treated several reactions. I also had a very strong caffeine reaction which he never picked up, but I found myself after much trial and error. On the whole it was definitely worth it though, as I could never have picked up all the foods I was reacting to through elimination and trial and error alone.
My brother had a blood test for food intolerances at a well known private clinic specialising in such tests, it was totally useless and did not pick up his reaction to eggs and soya, which was subsequently diagnosed and treated by the kinesiologist.
The symptoms you describe sound pretty clear though - it might be worth reading up some case histories (start at the library, or books in health food shops). Cows milk is the commonest food to react to, (and can cause eczema) and it might be that by cutting this out, you could solve the problem for once and for all, without going to the trouble of having tests. If you do this, and your child IS reacting to more than just cows milk, you might see a temporary improvement as the body celebrates getting rid of the daily dose of cows milk, then a recurrence of the symptoms as it readjusts to still being hit with other "bad" foods.
Good luck with getting rid of your son's skin troubles!