I have had a few birds along the way that fit your description. It sounds to me like, yes, she has some respiratory issue from the heat. I use Tylan injectable 1ml down the throat to take care of that. In 2-3 treatments, they are back to running and eating. However,.... the off balance thing sounds like you have another matter in this. It is my experience that when they start the wobblies like that, that they don't bounce back. It isn't always worth the time and effort of sending them off to necro either unless you just HAVE to know.
I hope she rebounds for you. If you haven't treated her with anything, I am 110% behind the treatment I suggested. I know it works on chickens and turkeys alike, except the turkeys need a high dosage due to size. For juveniles I use .5ml