Did your indoor-only cat seem to pick up an upper respiratory infection when she was at the vet? Many people who see this happen think that, and it makes sense, because they were fine before they went to the vet, and they're not otherwise exposed to strange cats that might be carrying something contagious. However, Dr. Patty Kuhly has a different explanation for it.
According to an answer she gave on this very question in the Miami Herald, it's more likely that your cat was already carrying the virus. Her visit to the vet, especially if she was there for a procedure like a teeth cleaning, could have stressed her enough to re-activate the virus.
VCA Hospitals has more information about upper respiratory infections in cats on their site. The virus in question is feline herpesvirus, and once a cat is infected, it becomes a lifetime carrier of the virus, even if it never gets another infection. However, if another infection occurs, then the cat will be contagious again.
VCA also says that mother cats can pass the virus onto their kittens, and they can become infected shortly after birth. So if you have a cat with an upper respiratory infection, there is the possibility that she's carried the virus her whole life, even before you adopted her. Or that she contracted it at the shelter, or somewhere else, before you adopted her.
You'll know your cat is sick because she'll have a runny nose, she'll be sneezing and lethargic, and she'll probably also have runny eyes. You should take her to your vet for a firm diagnosis, but treatment is often just for the symptoms. As long as you take her to the vet so you can be sure what's wrong with her, and you give her the proper care, she'll recover. But keep a close eye on her to be sure she's not getting worse or developing complications (such as eye ulcers).
If you have other cats in your house, they'll be at risk for getting sick, too. The virus doesn't usually survive very long when it's shed—a few hours at most—but it's enough. Plus, because it lives in discharge and saliva, simply touching noses, drinking from the same water bowl, or washing each other can transmit the infection. To reduce this risk, try using a bleach solution to disinfect any surfaces that might be contaminated. According to VCA Hospitals, bleach is a very effective disinfecting agent for this particular virus. However, only your other cats are at risk for catching it. People and other pets in the house will be fine, since cats can't pass this virus onto us or other animals.
So if she's come home from the vet, and a few days later is sick, she may have caught it there, but it's more likely that she was already carrying the virus and the stress of her procedure reactivated it.