My Bam had a respiratory infection last summer. Vet put him on Bactrim for two weeks. He got no stomach problems from that. The respiratory infection cleared up very nicely. Bam was the same as you describe your bun -he made funny breathing noises when he was agitated.
We’ve had many, many buns on antibiotics here. There are bunny-safe antibiotics, and then there are antibiotics that absolutely can’t be given to rabbits. Here’s a list of safe antibiotics: http://www.medirabbit.com/Safe_medication/Antibiotics/Safe_antibiotics.htm
(Medirabbit is a trusted source of medical rabbit info).
There is as you say always a risk of GI complications with antibiotics. They are tough on the gut microbiota. Many vets recommend you give your bun a probiotic while on antibiotics. There are many different kinds of probiotics suitable for rabbits, depending on where in the world you are. Benebac is used by many of our members, it seems to be the most easily obtainable one.
Some antibiotics have inappetence as a side effect. You should keep an eye so your pair don’t go off their food. If they do, you might have to support feed with Critical Care or other recovery formula.
A respiratory infection in a rabbit can progress from the nasal cavity down into the lungs and cause pneumonia, and/or go via the ear trumpet into the middle ear and cause an ear infection inside of the tympanic membrane. This is of course things you’d want to avoid. If your buns have had these respiratory problems for more than 10 days and it seems to get worse rather than better, antibiotics seems justified. You are very right about avoiding overuse of antibiotics. They should not be used carelessly. But when the patient has an infection that the immune system cant clear on its own, it’s wonderful that antibiotics exist.
Thank you for adopting these rabbits ?