What does my dog have allergies to? Food or Environment?

[Jen s]

I have a 1 1/2 yr old female boxer with itching everywhere - face, back, sides, paws, neck

She was fed Royal Canin large breed puppy until I realized it wasn't good.
~6 1/2 weeks ago, I switched to Innova Evo
1 1/2 weeks later, she was boarded at the vet for 5 days (vacation), and they told us she was losing too much weight on the recommended feeding guidelines (2 cups/day), so they doubled it.
I wasn't sure about feeding her that much protein, so I bought regular Innova to mix with Evo.
The next day, I noticed the sensitivity and itching.
A week later, I took her to the vet who dx her with allergies, put her on Prednisone, Hydroxyzine, Cephalexin for sores, and soothing shampoo.
She got better immediately.
1 1/2 weeks later when the Prednisone was tapered, her itching returned. The Hydroxyzine doesn't work. The only vet derm that's not in town does $700 allergy test to airborne allergens only.
I thought Innova was hypoallergenic; I don't want to feed her Royal Canin again.