Ok, I figured it would be Baytril, just wanted to confirm. Baytril is a broad-spectrum antibiotic; while there are others in that category that are suitable for small animals (after bad experiences with my first sugar gliders and Baytril (they hated it and it killed my bonding attempts with one of them), I was able to request a different antibiotic the second time I had a glider get prescribed one), Baytril is by far the most commonly given.
Unfortunately, you shouldn't count on the Baytril actually working... though ofc you should give the full course even if it doesn't appear to be helping, as "always finish the course" is a cardinal rule of antibiotics (the obvious exception being if it causes dangerous side-effects). You might get lucky and clear up the infection with a round of Baytril, but it seems fairly common for URIs to be resistant to it.
[That's not to say I question your vet's choice to use it, mind you! Rabbit savvy vets pretty much always whip out the Baytril for the first round of URI treatment and there IS a good chance it will be effective... there's just also a good chance that it won't.]
If she's not 100% better by the time you've finished the Baytril, you'll want to take her back in to the vet. At this point, the common options are to try another round of Baytril, to try a different broad-spectrum antibiotic and/or to do a culture (which determines what antibiotics the infection is resistant/susceptible to) and treat with a targeted antibiotic.
Don't get discouraged if this first round of treatment isn't effective - it's not at all uncommon for it to take a few rounds (and some trial-and-error/culturing) to fully cure a URI. As long as she doesn't get significantly worse and her eating habits and breathing aren't suffering, there's no cause for concern - just stay on top of medications and vet visits until you find something that works.
I don't remember... have I mentioned probiotics? If you weren't given one, I highly recommend asking the vet about it... if they don't carry them, you can buy something like BeneBac Plus in some pet stores and feed stores; failing that, it's extremely easy to find online (heck, I sell it on my site). Baytril, like all broad-spectrum antibiotics, is pretty nasty - it targets indiscriminately and can kill off good bacteria in the digestive tract, leading to serious side effects like nausea (which can cause a bunny to stop eating and develop GI stasis) and diarrhea. Probiotics should always be given with antibiotics (though not within around 3 hours in either direction of an antibiotic dose) - they negate (or failing that, severely reduce) the side effects of antibiotics.
As for the eye drops, I'm not familiar with those or with using eye drops as part of URI treatment... but then, I'm hardly an expert on URIs. I found information on
Medirabbit that says "Cephalosporin/tobramycin (both should be use in injected form only)" and Tobramycin isn't on this list of
rabbit-safe antibiotics (also part of the Medirabbit site);
however, I suspect the warning is in regards to it being unsafe to give orally, not about the safety of using it in eye drops. The
HRS site's page on antibiotics
(which, while it doesn't seem to mention probiotics, also has a great explanation of the potential side effects of antibiotics that probiotics can counter) DOES list Tobramycin, citing it as *unsafe* to give orally or by injection but *safe* in eye drop form. HRS completely revamped/updated their site within the last six months to a year (more recently than Medirabbit). I also found mention of Tobramycin eye drops being given to a rabbit on BinkyBunny's forum and in a couple other places.
I haven't found anything on using eye drops for a URI in rabbits (when eye issues weren't also involved), but I did find something about a guinea pig's URI being treated with Tobramycin eye drops in addition to an oral antibiotic. I haven't found anything that makes me think they shouldn't be given to a rabbit for a URI (ie it's contraindicated), but I also don't know if that's actually an effective treatment.
The fact that your vet prescribed the eye drops right off the bat in addition to the usual Baytril may suggest that she's experienced with rabbit URIs - they tend to have to be treated very aggressively, often with a combination of antibiotics, so a two-pronged attack right off the bat indicates a savvy vet *if* said attack is a viable one for a URI (which I honestly can't determine one way or the other in this case).
My guess as to a possible reason behind prescribing the eye drops is this: the Tobramycin in the eye drops will make it into the blood stream and therefore be distributed throughout your rabbit's body (including her lungs). Eye drops are being used for a respiratory infection simply because that's the only safe way to administer Tobramycin, which isn't given to rabbits often and is fairly unlikely to be resisted by the bacteria. This sounds iffy, but that may just be because I know little about it; the "iffyness" being due to the fact that Wikipedia says that when Tobramycin is being used for systemic purposes, it needs to be injected into the bloodstream or muscle (neither of which is safe for a rabbit, of course) and that ophthalmic formulas (ie eye drops) have low systemic absorption (meaning they're fairly ineffective for infections located in an area other than the eye(s)). That's specifically in regards to human use, though, and for all I know it could be different for rabbits.
At any rate, it appears the eye drops are reasonably safe for rabbits (as in no more unsafe than any other antibiotic approved for rabbit use), so I see no reason not to use them as they were prescribed.
As for getting them into her eyes, have you tried flipping her over and holding her on her back in one arm (the way you might for nail trims)? With human children who are squeamish about eye drops, parents often have them lie on their back as a means of making the drops easier to administer and I suspect the same trick might help for rabbits. Even without being tranced (a practice I don't recommend), a rabbit tends to be far more compliant once you have them fully flipped.
(If that's something you'd be up for trying but you're not used to flipping her on her back, I've got a video I made that shows how I flip my rabbits over that I can share.)