I went through the NAET process maybe 10 years ago in an attempt to reduce asthma and a whole list of sensitivities/allergies. I wish I could say I noticed a beneficial result, but since then I have good and bad days, weeks and months. There is no noticable connection to the expensive treatments or stringent protocol I had to follow.
I suppose it's possible that only one person knows how to do the process correctly, but I am really skeptical about such claims. I mean, how could that possibly be true, and why would that one person somehow capture the magic but not be able to teach others? I have tremendous respect for alternative medicine and most of the healers I have met, but some are snake oil salesmen, and claims like "I'm the only one with the real cure" are often the tip off.
(Interestingly, some who sell snake oil do seem to believe that's it's the real deal. And sometimes enough belief results in a temporary or permanent cure. This may be faith healing or the placebo effect. Whatever it is, if it works, I say go for it!)
Like your son, I can't have scented anything in my surroundings, and am frequently driven out of public places by people wearing toiletries and perfume. I have adjusted to the rather extreme restrictions in my life, but I sure wouldn't wish it on a child.
Since you are desperate, you might want to consider a naturopath, who will employ a gentle and sensible approach, probably much more doable and less expensive than NAET. I would imagine there are some who specialize in working with children. The results may not be instantaneous, but may lead to a healthier and more comfortable child.
I've also had some remarkable results from homeopathy for specific complaints. And I have loved how much better acupuncture makes me feel after each treatment. It doesn't claim to be a permanent fix, but can help put us in better balance and able to handle the normal assaults on our bodies more effectively.
Another thing I've learned about skin, lung, and stomach sensitivities is that they can be made worse by, or even caused by, stress. It might help to keep a brief "emotional diary" of the kind of day your son has had, what sort of social contact or other stimulation, whether his sleep was good – anything notable. (Note whether YOU have had an unsually stressful day, too, since that can affect your children.)
Rate his symptoms each day. Watch for patterns. You may learn that you have ways to smooth out his emotional highs and lows, and even his itching, by avoiding stressors.
Good luck. I'm so glad you care about your son's experience.