Hello. Your question has been released to me and I'll sure do everything I can to help you and your Grey. I have one in my flock and I know just how special they are. If I can get a bit more information from you, it will help me to give you my best advice.
Are you positive the vet you are working with is either a certified Avian vet or at least one that comes highly recommended for their Avian expertise and experience? Unfortunately, many dog/cat vets do not have that expertise. More unfortunate, there are a few who will not say so up front and let you get to someone who can really help.
I am suspicious because it's never good practice to just take "pot shots" at a bird with an antibiotic when we don't have a firm diagnosis. They don't handle antibiotics that well, even when there is a definite need.
Do you happen to know, or can you find out, the exact name of the antibiotic and the dosage that was given each time?
Did the vet weigh your bird prior to figuring the dose amount?
As you may know, when talking about birds, vomiting and regurgitating are two different things. Regurgitating is what they do when bringing up food to feed a mate, a chick or even for their human. It is proceeded by a pumping action of the head and neck, then a small amount of partially digested food comes up. It usually is swallowed again.
Vomiting usually has no real forewarning, the food comes up, they almost always shake their head, scattering it all over them and whatever is near by. Using those descriptions, is she actually vomiting?
Are you positive it is a female bird? Has she ever laid any eggs? If by chance you are not sure and if this is a Red Tail, (Congo) tell me if there are any real faint silver outlines on any of her red tail feathers. (This will not work if you have a Timneh.)
Have you seen a change in her droppings; color, consistency, amount?
Is she ever taken outside, like on a porch or deck for fresh air and sunshine?
Does she have a full spectrum lighing fixture?
Tell me about her normal diet and has she had any fresh fruits or vegetables lately that were not products of the U.S., that you know of?
This and anything else you think might be important will help me do my best for you. Patricia