Wow what a story!! Congrats on your new addition!! She is adorable and I love the name you picked for her.
I'm glad they picked you to be her new owner because who knows where that little girl would have ended up or what would happen to her if given to someone else.
Bordetella given via the nostril is a live virus. The shot/injection is a killed virus.
If she is still coughing I would say she has kennel cough now. I would take her back to the vet and get her some antibiotics bad sadly it will probably take a while for her to get over. That's why I hate the nasal bordetella, I've seen so many get KC from it.