Prednisone is a strong drug and very effective but it does have long term side effects. My first dog was fine on it but I was anxious the second time around so My Vet prescribed Atopica, which worked wonderfully. It also has possible side effects but is generally considered to be less dangerous than Prednisone. Another similar new drug is Apoquel.
My Vet didn't recommend allergy testing either but some people here have done it and been very happy they did. It is expensive. Another option, if you think your dog might have food allergies, is the
NutriScan Food Sensitivity and Intolerance Test for Cats and Dogs test. I did this recently. My dog does, as we thought, have mostly seasonal environmental allergies but as per this test there are a few, very few, foods he should avoid.