You won't regret the "better" dog food. We have a 15 yr old yorkie poo who used to scratch himself raw. Steroid shots would give some temporary relief, but the itching came back. I finally discovered a grain-free pet store, & it has made a huge difference!
His favorite dry is Orijen senior. But he loves canned food: Instinct rabbit & pork are great, the Merrick grain free stews are good. His New favorite is Red Barn with bully sticks in it. Sure hope this works for you!