Awe poor Blue. I am sorry it is difficult to pin down time with the vet and get what you need sorted.
When Peppy went to the vet after the New Year, I too had to wait in the car and correspond between the vet tech and a phone call. When I got the form after the appointment the entire history I explained to them had errors, like where Peppy came from or how old he was.. basically all the details were slightly off.
Peppy had a fungal infection and he shredded all of his feathers out from it. Poor little guy. He was an antifungal straightaway and didn't get any antibiotics. The antifungal medications are longer term term, and they aren't easy to administer for a zebra finch. So we added them to the water. And that in its self was a process because you need to dissolve the medication, but the medication is very sensitive to heat and will not be effective if too warm. We worked out a process, but it was probably the most complex treatment I personally had to give to a bird.
Infections are the worst.
I hope poor little Blu gets it all sorted soon.