If the respiratory problems continue for more than 3 weeks, you should check for Cryptococcus. My cat turned out to have Cryptococcus -- a potentially fatal fungal disease. When I got her from the shelter, she had what the shelter was calling just an Upper Respiratory Infection (URI). Many vets and many dollars later (I even got "fired" from one vet for being so persistent), a vet finally, begrungingly, checked for Cryptococcus, which she turned out to have. The test is expensive (about $130), but worth it, considering the disease eventually gets into the cat's nervous system and then paralyzes and kills the cat.
I then put my cat onto Fluconazole, an anti-fungal med, which is very expensive unless you go to one of the cheaper compounding centers, such as Cactus Pharmacy in Arizona. Apparently Arizona has some sort of drug cost limitations that help the consumer. The cost there was about $50 for a 1-month supply instead of the usual $200/month !!! Cactus Pharmacy: 877-971-3001. Now that my cat has been off the meds for 1 1/2 years and has tested negative for the 3 Crypto tests taken since going off the meds, she only has to be tested once a year.
Nowadays, shelters and vets are more aware of Cryptococcus, and some check for it as soon as a URI lasts more than 3 weeks.