Rice is fine as far as allergens, but any carb will contribute to inflammation, which is something else to understand about GI issues. Once the GI is compromised, there are large particles floating around the blood stream that stress out the liver and confuse the body's normal immunity, leading to auto-immune responses.
Based on your other posting regarding eating grass (which they will do to improve their gut flora), I'd guess she isn't feeling too great. You might want to add anti-inflammatory supplements (Salmon oil/coconut oil, no flax or seed oils like Canola oil) and a broad spectrum probiotic. The "medical dosage for Salmon oil is 1gram/10 lbs of dog. If you aren't already trying to address the inflammation issue, this is where I'd start.
I know you are doing your best given life's constraints, but TOTW has MANY ingredients that are questionable. Canola oil, guar gum, "Natural favoring" (aka MSG), peas and beans (legumes), eggs, and tomatoes all may cause problems, especially for a compromised system.
If you really want to get to the solution, I'd strongly recommend contacting a local raw feeders group to get a mentor to help you with a month of "ultra, clean, raw" Prey Model feeding. Then add back veggies, dairy, and other allergens slowly. A month isn't a really long time, and you'll probably notice differences the first week.
Feeding raw will also be cheaper than feeding TOTW, if you spend the time to talk to someone with experience. And it will save you time and (vet?) expense to figure out the problem sooner vs later.