Of course you did the right thing, as others have said. The illness is not fully identified - usually when a virus doesn't clear up, doctors say, "Well, maybe it's bacterial after all" and give out antibiotics. If it's a virus, the antibiotics won't help. But if it's a bacterial infection, getting started sooner is best. While the antibiotics won't work in a short period of time, at least they'll get started! So why wait? The doctor had no way of knowing that your daughter would take such a quick turn for the worse. And if you had called her, she would have told you to start the antibiotics sooner, just as you did.
FYI it's important to finish the entire antibiotic treatment, even if she feels better in a day or two. Otherwise she'll just get sick again. My mother was virulently anti-medication, and never ever let her kids finish the whole treatment. As a result, we were sick A LOT, never well for more than 3 weeks over a 2 year period. I don't believe in unnecessary medication, not at all, but I absolutely believe in finishing the whole course of antibiotics.
Hope she's on the mend soon.