A couple of years ago, we went gluten free for a bit. We went cold turkey and removed anything that contained gluten in it out of the house. We couldn't budget pre-packaged gf foods, so we had to make everything on our own (except the pastas, those we did splurge on). The only difference I saw in the kids, especially my son, occurred too quickly to be attributed to the gf diet. After looking at what we ate we realized that all preservatives, dyes, etc. had been removed as well so we put it down to that and removed even more from our diet even when we went back to eating gluten. I still buy minimally processed foods, make most of it on our own, eat as much local and/or organic as possible, etc.
Fast forward to now. I recently, a couple of months ago, had a scan done for my oldest son, J. He has a ton of behavorial issues that have us concerned. He's 9, almost as big as I am and he had started getting violent. We didn't want to medicate him at all possible so we decided to see once more if it were food related. After the scan was done, it told us what t he foods and other substances (such as dyes, preservatives, etc.) he was most sensitive too so we could avoid them. Note I didn't say allergic; he's not. The worst offenders on his chart was soy & corn. Do you have any idea just how much corn & soy is in our diet, even when you don't realize it? It comes under many different names and shows up in the most unlikely of places. Trust me, I know. Pretty much when I go to the store now, I pretty much bypass 90% of it. Since in addition to the no soy or corn, J had to go on a low glycemic diet it has radically changed our eating habits. Since we've done this, we have seen a large difference in J's behavior. He's nowhere near a perfect angel but he doesn't have the huge rages he has had in the past. Oddly enough, his hair has also gotten softer! It's felt like a brillo pad for years and I'd almost forgotten how downy soft it used to be. I had just attributed it to his genes and him getting older. I had no idea his diet would have affected it that much! Also, we can always tell when he's had something he's not supposed to or if it's in the wrong proportion/ratio (such as in a low glycemic & low carb diet) but within an hour or so he really starts acting out.
SO, as to your son, before you start elimination diets you need to first, get him a much more rounded and balanced diet. That could actually be part of the problem right there. Where is his protein? That is a major building block, especially at this age! Two, you need to talk to your doctor as well as a licensed nutritionist. Never start an elimination diet without speaking to them first so they can help you. I would have been absolutely lost without J's nutritionist, especially as much as we had to change; she gave us a basic menu to get us going. J's nutritionist is also a naturopath and she had me give him several supplements, Natural Calm (for the magnesium), digestive enzymes as well as probiotics. All of this combined together to make a huge difference in J's behavior and well being.
Every child is different and he could be insensitive to the oddest things. For instance, on J's list, besides the corn & soy, is peaches, wild rice, eggs, buck wheat, quinoa, etc. It's all in varying degrees so depending on how high on the list they are depends on whether he can a little in moderation or if he had to cut it entirely. The other thing that's really high on his list is chocolate. He can't have it at all, poor little guy. :( Oddly enough, my mother reminded me that I absolutely couldn't stand chocolate when I was pregnant with him. She said I turned green just smelling it. Of course, the idea is for us to introduce these foods back into his diet eventually (since he's not allergic to them) but it will be some time in the future before we do so. His body needs the proper nutrition on a cellular level first. He's extremely low on all of his vitamins & minerals and he's actually experiencing a form of leaky gut so his whole system is out of sync and the easiest way to describe it is that the body is trying to fix itself but doesn't have the means to do so so in actuality is making things worse. Make sense? So an elimination diet can and will work, you just have to start in the right direction. You will have to do a lot of experimenting to find the things that may be affecting your son.