Fish oil intolerant corgi with other GI tract issues from food coming up. Food options?

Looking for advice on food options for my 10-year-old Corgi who has been dealing with food sensitivities.

Here's what we've figured out so far:

- She’s been allergic to fish oil and fish products her whole life. It causes itching, redness, and what appears to be hot spots.

- She tolerates homemade cooked chicken and rice but commercial chicken-based dog food gives her diarrhea.

- We tried a hydrolyzed prescription food and her digestion improved, but it contained fish oil and her skin flared up again eventually. We told the vet that this would probably happen, but he thought it wouldn’t.

- She's currently on carprofen for arthritis

We know she can't stay on homemade chicken and rice forever. We're trying to find a commercial or vet-prescribed option that works for both her skin and her stomach. Any input appreciated!