Long story short, the vet was wrong. His diagnosis was based on the negative results of two tests that were done by a different vet office, and when he repeated the tests at his office, they were both positive. Once she started on meds to treat these other issues, she immediately started to improve, and now she acts like a normal, tiny puppy most of the time. We are still feeding her very frequently, just to be safe and help her gain weight. She weighs one pound now, so she is putting on weight.
Thanks for all of your prayers!!!