She sounds like my Samantha who was allergic to many things including 4 types of grasses, 4 types of weeds, cats, dust and storage mites, fleas, all dairy except eggs, corn, beans, lamb...are a few that I can remember.
I do know my vet said if they have too may allergies that the shots will not help. I still decided to try the shots for Samantha and as my vet said they didn't help. The only thing I could do to give her relief was to keep her on the lowest dose of prednizone possible. I knew (or thought) it would shorten her life but knew it would give her better quality of life. She was 3 when she started on them. She lived to be 14 yrs, 2 months, 2 weeks and 5 days. I found I was able to keep her comfortable on about 10mg every 2-3 days. Good luck. Allergies suck.