Cats can get respiratory infections, and yes -- she could have picked it
up at the vet's.

Has she had her distemper pack shot? That usually includes vaccines
against the two main viruses that cause respiratory infections in cats.

Keep an eye on her and make sure she keeps eating enough. Cats stop
eating when their noses get stopped up. They don't eat if they can't
smell. That was a crisis point when one of our kittens had a respiratory
infection.

Talk to your vet, some want to give antibiotics in case it turns into a
bacterial infection (but the main problem is usually viral.)

Take care,

Rhonda