The vet is the one who is supposed to have the baytril already mixed in saline. If you think there is a mistake, take it to the Vet and confirm. Dont try to mix it yourself.
Baytril does burn, but like most have said, it's from higher concentrations.
Also, Baytril can be given in other ways, by nebulizer and also orally. The concentrations are different, and I don't know that much about it.
People say, that for snakes, it's just most effective given by injection.
If you worry at all, call your vet up and see if they will demonstrate again for you. Maybe Becki will chime in with some advice.

[edit] I didnt read the whole thread, you've already talked to the vet. My bad