Have you considered food sensitivity testing?
These tests are unproven, and thus must be ordered through a naturopath; however, based on my experience with these tests, they have been very helpful in identifying the problem. They are about $100, and test many, many foods as well as common allergens. You can also get a vitamin/mineral test, which I would also recommend. The tests I did were the IgG Food Antibody Assessment by Genova Diagnostics, and the NutrEval test also by Genova Diagnostics. When I first took these tests about 2 years ago, my acne looked similar to your son's, though a little less inflamed, and more on the forehead. Serum levels of a large number of vitamins and minerals were low; I had high sensitivities to wheat, soy, peanuts, and a few other things; my gut flora was out of whack (I did a stool test as well). The naturopath I was seeing put me on a restricted diet and gave me some herbs and probiotics to help with gut flora.
ow at the time, I thought the whole process was silly; there was really no evidence for any of her 'treatments' in scientific literature, and, being a scientist, I had more faith in the literature than in a quack naturopath. I didn't think acne had anything to do with diet. In fact, I dismissed the naturopath's claims outright at first, and while I took the herbs and probiotics, I didn't really change my diet.
Anyway, here I am two years later. The transition to a paleo-esque diet has been hard, and it took a long time to get used to. It's really only been the last few months that I've been very serious about avoiding the foods I tested to be sensitive to. Last week I took the food sensitivity and vitamin tests again. Everything has improved drastically. I have almost no reaction to wheat, peanuts, and soy; my serum vitamins are within the norm. Most importantly, though, my acne is about 90% better. Not gone - but much, much better. It doesn't look like I have acne any more, unless you get up close.
I've tried a lot of things. I've probably tried just about everything short of accutane. Some things helped, other things didn't. What I can say for sure is that my acne did not improve because of topicals. In fact, my topical regimen is extremely limited - I only wash my skin once a day with a salicylic acid scrub (this I have found to help, which is why I am continuing it) and I do not apply any medications or moisturizers (I occasionally moisturize, but maybe only once a week).
The real turning point came just a few weeks ago. Up until then, I would get spots on my chest after eating something that I was sensitive to. I went to Minnesota last weekend, and was unable to adhere to my diet; I ate soy, I ate wheat, I ate everything and anything, muffins, donuts, pasta, ice cream etc. Not a single spot. It seems as though my gut has healed enough to prevent some larger food antigens from entering my blood. I began consuming bone broths via soup about a month ago, and I think this is how I healed.
Of course, this was in combination with a safe diet. And it took me two years (though I didn't have all the tools at my disposal that I do now for the majority of that time).
I would really recommend getting testing done. It's easier to solve a problem if you know what needs to be fixed. And you'll probably save money in the long run. Until then, though, paleo diet (rice is okay though) with a strong emphasis on bone broths (use hamhocks and beef bones with some vegetables and spices, get the joints and tendons too, add 2 tablespoons of apple cider vinegar, let it simmer for 18-24 hours) will probably be immensely helpful. Vegetable juice would also be good (carrots, kale, celery, cucumber, a little green apple, broccoli, etc). A perfect meal would be a chicken, vegetable (cherry tomato, onion, celery, cauliflower, carrot, spinach), and rice soup in bone broth with a glass of vegetable juice.
I think it's important to note that probiotics could make the situation worse if your son has a compromised gut barrier. Gut microbes are often behind forehead acne, so it might be good to stop those for now. If you want to cover all the bases, order a stool test from the naturopath as well. If there's an overgrowth of a particular bacteria, removing it could drastically improve your son's acne.
Now that I've written all that, I noticed that you mentioned itchy skin. This can be two things. The first is an IgE reaction to food antigens - so, leaky gut. In this case I would recommend testing for food sensitivities, and all the other stuff I mentioned above to heal a leaky gut.
The second is fungal folliculitis. It's possible that this is a topical infection - NOT acne. You can test this by washing with an anti-dandruff shampoo; I would use head and shoulders with zinc pyrithione; apply in a layer in the shower, leave it on for ~3 minutes, wash off - make sure it all comes off, otherwise you could get lots of irritation. If it's fungal, it will respond within a couple days, and be drastically improved within a week or two. Note that zinc pyrithione is also antibacterial, so it will improve normal acne as well - just not as much, and not as quickly, and not as completely. Using a shampoo on the face can be quite irritating, so it would be good to moisturize afterward. Like I said, I tried everything
My bet is still that it's the first option, though, so if you want to test the head and shoulders shampoo, I would do it in combination with bone broth/restrictive paleo+rice diet in addition to getting the three tests mentioned - food antibody and vitamins (which are both blood tests), and stool.