Chicken and rice is not a balanced diet, infact, if you dont get other nutrients in her, it can cause all kinds of problems.I cant see how a dog can be allergic to dog food in general..that's impossible.It's more likely that she's allergic to a certain ingredient in certain brands of food, so your job is to find out what ingredient isnt agreeing with her and find a kibble without that ingredient.
Milo (my male) had skin problems when we first got him.The hair on his face and paws would fall out and he'd eat away at his own paws due to the itching etc, so we had his vet run some tests and it turns out he's allergic to grain...an ingredient present in 90% of the kibble on the market.
Once we started him on a grain free diet (there is kibble for almost every allergy out there these days) the issues went away.
I'd ask your vet to run some allergy tests and see what hapens fron there, because no dog is allergic to every ingredient present in kibble or every brand on the market
What surprises me the most, is that your vet has told you to find out what she's allergic too and that you are the one who has to find her something that wont give her diarrea or she'll die.....? I think your vet needs to do a better job.He can't can't expect your dog to live entirely on chicken and rice and he can't expect you to rule out all the things that give her diarrea...he needs to get his finger out.