Sorry, I should've been more clear – Novel proteins are meats that your dog has never eaten before... For example, if your dog has primarily eaten chicken-based food over the years, they could develop an intolerance to chicken in adulthood. Chicken, beef, and lamb are common in most commercial dog food (check list of ingredients -- often, even if they say a food is one thing, it'll still contain other ingredients like chicken fat, etc.). Anyway, if your aim is to do an elimination diet, you'll have to find a "novel protein" that Mongo has never had before to start with.
In our case, we fed the Primal Raw turkey & sardine recipe for two full months:
Not sure what the availability is like in Canada, but there are other brands too. The food itself was a bit pricey (most commercial raw is spendy), about $60 ~ $80/month. But yes, cheaper than meds and repeated visits to the vet! Bowdu took to it quite easily, and it did make a difference in the long run, if only to encourage his appetite and interest in food. Once we got used to raw meats, and I had some time to read more about raw diets, I moved to home-prepared meals, which is significantly cheaper. And because I don't have all the time in the world to make food for my dogs (I wish!), I reintroduced high-quality, fish-based kibbles for morning meals. So now we basically do kibble in the morning, and then a variety of stuff in the evening for dinner, with an emphasis on lots of fresh food.
I like Dog Food Advisor for researching commercial dog food brands (they also review dehydrated foods, raw, wet, dry foods):
There are lots of good books and websites on raw and home-cooked recipes too. Here's just two that I've spent some time with:
As an immediate remedy, you can try adding fish oils to his diet to boost skin health. I give the dogs the same stuff I take. 1000 ~ 1200mg capsules, once a day, paired with just a bit of Vitamin E oil (if you can get it in dropper form, 2 or 3 drops / Basenji should be sufficient).
I think quick baths are okay if you're dealing with environmental allergies. Even if it's just a gentle hose-down with plain water, no soap. I use baby wipes every day during spring and summer, which I think also keeps some of the allergens away. Multi-pronged approach, to be sure!