Allergies to things in the environment are much more common in dogs that true food allergies. Seasonal occurrence can be a clue to that, but some allergens may originate within your household, or be brought in from outside (especially if you clean as well as I do
Identifying a true food allergy with food trials can take months. You switch to a hypoallergenic diet for a month or even longer...if symptoms go away, you add proteins back into the diet one by one at a very slow rate and look for the symptoms to recur. There are skin tests and blood tests too, all of which are not necessarily accurate, especially if the dog has been on steroids recently.
Intolerances to various foods occur at a higher rate that true food allergies. So it can be worthwhile to try different dog foods with different protein sources, though it can be tricky to find foods that really don't include a variety of proteins, even though the label says they only contain a few. For example, animal fats, generally from a variety of sources, can contain some protein too, and if your dog is very allergic to a particular protein source, even the small amount of protein in the fat can make him react. And food manufacturers don't necessarily clean their equipment between different kinds of food, so you can have cross-contamination.
It can be a bear to identify and then treat skin problems in a dog. That's why I'm thinking that a visit to a dermatologist might be worth it for a recurrent skin problem, if your general vet hasn't been able to get to the root of the problem and find a treatment which seems to be effective over the long term.