I have met a lot of people in the same boat as you (including myself). There are several things you need to keep in mind with allergies:
1) It's just like with people - dogs can be allergic to weeds, grasses, trees, foods, fleas, dust mites, etc.
2) Allergies get worse over time and your dog will pick up new ones as it gets older.
3) If you know or can find out what your dog is allergic to you can avoid it (or you can get the allergy vaccines - but would need that testing first) and that will help. The allergy test your vet mentioned will help if your dog is allergic to plants, mites, fleas but NOT if he's food allergic. Changing the food only helps if you do it right - you would need to talk with your vet to find out how to do a food trial with him.
4) Take the dog to the vet as soon as a flare up starts. Don't wait for it to get bad because then you'll need more medicines for a longer time. (And it will $$cost$$ more.) There ARE medicines other than steroids that you can try - antihistamines, ectc. - but you need to have your vet tell you the proper dose. (NEVER EVER give a human medicine to a dog without talking to the vet first.) And if there is a bacterial or fungal skin infection (starts because of the allergies) treating those will be necessary to help him feel better.
I hope this helps. Keep working with your veterinarian to come up with a plan that works for your dog and fits in your budget. Allergies are frustrating, but there are always other things you can try. (Even dog dermatologists if you need more testing than your regular vet can offer.)