Upper respiratory infections like Jbun said can be very serious, I don't mean to scare you but it could be Pastuerella and if it is, Baytril isn't a very effective antibiotic, its an older antibiotic and many bacteria have become resistant to it and a lot of Vet practices are phasing it out. So if your Bun is not better in 7 days or if it gets sick again follow Jbuns advice and go to a rabbit savvy Vet. I don't think there is anything called New home sniffles and your vet is really down playing it. I'm going to quote some advice given by a retired moderator on this site that I think really knew his stuff- His name is Randy and he ran a wildlife rehab center and worked with a Veterinarian who was a rabbit specialist and treated a lot of infections in rabbits. His antibiotic of choice is Azithromycin/Zithromax. He doesn't recommend Baytril.
This isn't entirely accurate. Yes, in some cases baytril may prove ineffective, but that is true of any antibiotic. These things depend on the type of bacteria involved and what antibiotics it is sensitive to, and any antibiotic resistance. So it is the bacteria that can become resistant, not the rabbit getting used to it making it ineffective- same with the bacteria that affects us and antibiotics. It can become resistant through overuse and incorrect use. Not all URI's are from the pasteurella bacteria either. And many people have found baytril to be effective for URI problems in their rabbits. It's considered one of the safest antibiotics for rabbits, so is generally tried first to see if it helps. If not, other antibiotics like penicillin and Zithromax can be tried, but with Zithromax you are also taking on the high possibility that your rabbit will stop eating, as this is a common side effect. And even zithromax may not be effective, depending on the bacteria involved. A culture and sensitivity can also be done to see what antibiotic may be effective.
Though 'new home sniffles' isn't a technical term, it is something that can happen with new rabbits when brought into their new home. They are in a new environment. They can be sensitive to new chemical smells, dust, as well as the effects of being brought into a warm environment if they are used to a colder one. But also the stress from being brought into a new home can cause an essentially 'dormant' bacteria to emerge, because the rabbits immune system is weakened from the stress, and this can lead to a URI. So when these 'new home sniffles' or nasal discharge occurs, it needs to be determined whether it is from a sensitivity to something in the new environment, or if it is from a bacterial infection.
7 days though, is a
very short course of antibiotics to be using for a possible URI. A 14 day course would be much better, and the antibiotic should be continued for several days after symptoms cease. So if runny nose/sneezing is still occurring and your antibiotic is almost finished, you may want to ring the vet for an additional 7 days worth. Then if there is no improvement at all, try a different antibiotic. But this is no easy thing to clear up usually. If the baytril seems to be helping but it doesn't clear up in the 7-14 days, then you may need to do another 14 day course.
http://www.bio.miami.edu/hare/sneezing.html