For arthritis - They can do xrays to confirm. We have Tyson on Nujoint DS - edit, we also give him Tumeric which is a natural anti-inflammatory and we just started Adequan injections 2 weeks ago. I'm against having him on drugs if there are other options. So we choose injections for now, and possibly laser if needed. But Tyson is 9. I think maybe some supplements for her since she is young may help out.
Prednisone - I personally would not keep her on that. Its a strong med with alot of side effects and if used long term can affect liver, heart, and kidneys. I would ask your vet about Apoquel instead. That is alot safer, and you can save the Prednisone for an emergency case or bad breakout.
Back to allergies, what are you currently feeding her? I know you mentioned different diets, but what is she on now?