The other one is probably Cephalexin. It's used for puncture wounds(Ask me how I know that and why I have a stash of it on hand at all times!)

I've had two dogs with this same type of infection after a simple puncture wound. One from a fight and one from poking herself on a stick! My vet never mentioned putting them down. He did say it was very serious and had to be treated aggressively. IV antiobiotics were an option if the pills didn't work fast enough.

Did he give Baby anything for pain control?

I hope she responds well and quickly.