Our dog has been losing fur on her chest, belly, inner sides of her legs and having hot spots and loose poops many times a day... which makes me wonder, is your dog having squishy poops? Is he pooping a lot? Those are common in food allergies. Dogs without a food allergy poop on average about 1.5 times a day, and dogs with sensitivity to their food usually poop more often. Our dog was having big, squishy poops about 4-5 times a day. That would be a good way to identify if it is a good allergy. Also, just a guess but going off of basic biology here, if there is a pretty symmetrical reaction that means it is a systemic issue, not something with physical contact. For example, my dog was losing fur all along her chest and tummy, and the inner sides of all legs. She had random itchy spots and hot spots yes but she had this hair loss reaction symmetrically, which means it is something systemic ie. food, inhaled, vs. contact with something or mites or fleas. This along with her poop trouble are all indicators of an issue with an ingredient or multiple ingredients. One of the most common, if not the most common, food sensitivity is usually a protein source like meat or ingredients from a particular species. For some reason the body particularly likes to form over-reactive immune responses to certain types of proteins in particular, this is true in humans with food allergies also. These immune responses often develop with over-exposure to an ingredient, and with many dog foods containing much of the same ingredients it is easy for a dog to become over-exposed to things.
So, the best thing to do is to try to cut out common ingredients dogs have allergies with, namely the common animals: chicken, turkey, beef, pork. Lamb used to be a go-to for allergic dogs but now with it becoming more common in dog foods it is causing allergies in more and more dogs now, too. The problem then is that some dogs also will have allergies to animals similar to the ones they initially developed an allergy to, dogs with an allergy to beef are more likely to have allergies to bison and buffalo. Dogs with an allergy to chicken are more likely to have an allergy to duck. Not always, but some have that tendency.
The best thing to do is find a very simple food with only source from one animal that is less likely to cause an allergy, we chose salmon. Then we eliminated foods with wheat/corn/soy because those are common problems for dogs, too. We also chose to eliminate grains. It is important when you do this that all sources of the dogs food avoid all those ingredients... make sure the treats comply with this diet, no scraps etc. This what we are doing, and then we wait for a few weeks to see if she improves. If she does improve substantially then we know that ingredient is safe. Then, if you want, you can try to introduce another animal ingredient, one at a time, and try that for a bit and see if she relapses. This way you can see one by one what is safe for her.
I read probably around a hundred ingredients labels looking for a food that met my criteria that didn't break the bank. I ended up going with salmon as her protein source, since that is less likely to cause problems than many other animal meats. The oils in salmon are also good for the coat and for irritated skin, so that is a plus. Some people may want to introduce salmon oil or other irritation-calming oils or ingredients as a solution without substantially modifying the diet, but I personally feel that these will have a very limited effect, if any, if the animal is still being exposed to the ingredient that is causing the immune system to flare up. I'm just sharing with you what my personal process with this has been, if you do want to try reducing likely allergens in the food. I'm sorry if this seems pushy, it's just my personal plan after doing a lot of reading and reading many, many ingredients lists.
Personally, I chose this food: https://www.amazon.com/gp/product/B007CJ95TE/ref=oh_aui_detailpage_o02_s01?ie=UTF8&psc=1 the only animal it contains is salmon, and no wheat/corn/soy or grains. It is also reasonably priced. $38 for a 24 lb bag. I also do these biscuits: https://www.amazon.com/gp/product/B006QV1PRE/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1 again, only salmon, no other animal. And affordable. They do contain rice and oatmeal, which are grains, so maybe not that ideal but they otherwise fit into her new diet pretty well. We use these treats for training: https://www.amazon.com/gp/product/B0085NTR5S/ref=oh_aui_detailpage_o01_s01?ie=UTF8&psc=1 no animal products, however again they do contain oats, but I thought I'd give them a shot. We completely cut out scraps and make sure she isn't getting into the cat food anymore. She has been on this new a little over a week and she is already noticeably improving. She is barely scratching or licking at all anymore, her ears are improving from an ongoing irritation/discharge/infection, and her poops are firming up. We are waiting to see if her fur will begin to grow back.
Anyway, this is just an example of a super-cautious attempt at eliminating ingredients from her diet she may be having trouble with. Just wanted to offer my experience with handling all this, and what I have learned after spending a lot of time reading different aticles and varying opinions. although I am relatively new at this myself so I am by no means an expert.