Things to try
My dog has allergies and they started young. We went through all the mites, fleas, skin disease stuff too before confirming on allergies.
A few things to try short of tests.
1. Coconut oil- try this instead of fish oil. All the same good omega 3's and 6's, but if your pup has a fish allergy, this will be better. I just put a little scoop on his food and my dog loves it. It should be cold pressed organic. You can google the exact ratio, but it is like 1/2 tsp per 15 lbs. or something close to that.
2. sensitive skin shampoo- We use Aroma Paws sensitive formula, every other week bath. It soothes his skin, helps limit any allergens he picks up on his paws/coat.
3. Look at all your food and treats. My bet is there are a lot of different ingredients, particularly grains. Try to limit the ingredients and see if that helps things. For instance, we are using venison and sweet potato food and all his treats are either venison or sweet potato. Sometimes I will let him try a something else like a raw bone, but we avoid grains of any kind now.
If any of those help, you may be on the right track for allergies. There are lots of different tests (saliva, blood, skin) but most Vets will urge you to try #3 before allergy testing anyway so you might as well do that before you have to pay someone to tell you to do it.
There are also a variety of drugs to try, but you'll need a Vet to tell you the ratios of even the OTC stuff like Benadryl or Zyrtec for dogs.
Allergies are no fun but hopefully you'll find things that work and you can manage them.