If he hasn't had a complete work up with a pediatrician or naturopath I would suggest doing that first. As Bug suggested nutritional deficiencies can also cause these symptoms.
As to dark circles under his eyes, many people naturally have dark circles and there is no way of getting rid of them for some. My granddaughter has allergies and dark circles. Her allergist said to ignore the dark circles. She'll probably have them her whole life. Her mother, who does not have allergies also has dark circles.
When you say he has fluid in the ear do you mean he has chronic ear infections? If he doesn't have infections and it doesn't negatively affect his hearing I wouldn't be concerned about fluid in the ear. Has a medical person told you to be concerned? If not, I'm not understanding your willingness to go thru the torture of looking for allergies.
An elimination diet is much easier than a rotation diet. You start with a basic set of foods and add a new food each week or two. Look up elimination diet on the Internet.
Since you've perhaps narrowed it down to just the 3 or 4 foods, you could do a modified elimination diet and eliminate one of those foods at a time. This wouldn't be as accurate as starting out with a base and adding one food at a time but might still give you an idea.
I would hesitate to eliminate fish and flax oil from his diet as well as milk fat. He needs fatty acids for his brain to develop. I would try putting those nutrients into his diet by feeding him fish and adding flax seeds to his food rather than giving him pills. He can get necessary fatty acids from butter even when milk or dairy doesn't agree with him.
I urge you to not try to figure this out on your own. I'd find a naturopath, nutritionist. and/or a pediatric allergist who could help. The realm of nutrition can be very complicated.