Enrofloxacin and meloxicam are typically considered safe to give orally to rabbits, unless you have some different type of formulation than what is commonly used in the US/Europe, and has added ingredients that might not be safe for rabbits, like high levels of artificial sweeteners. But there is also the possibility in rare instances, for any person or animal to have a negative reaction to any medication. So though these are common meds generally considered safe for rabbits, there's always the potential for a negative reaction.
But in normal circumstances they're usually considered safe for rabbits and are 2 of the most common medications used to treat minor to moderate infections and inflammation in rabbits. I've had a vet prescribe both on many occasions to several of my rabbits with no ill effects. Though do be aware that meloxicam is a NSAID, so should be given when a rabbit has food in their stomach and is drinking well, as to minimize gastric irritation or irritation to the kidneys. And as a NSAID, shouldn't be given if a rabbit has potential or known, kidney issues or gastric ulcers. Also be aware that rabbits generally detest the taste of enrofloxacin, so it usually isn't taken willingly by them even when mixed in a sweetened suspension to give orally.
https://wabbitwiki.com/wiki/Common_drug_dosages_for_rabbits
It's your rabbit, so your choice. I've just shared my opinion of what I think the sign of possible white discharge likely is, but without actually seeing it for myself in person especially, I could be wrong and maybe there isn't actually white discharge. This could also be the possibility if your rabbit isn't sneezing more than normal and doesn't have matted fur on the insides of the front paws from wiping sticky discharge off.
But if it is an infection, your rabbit could go on for several more months without it worsening or causing complications, or it could suddenly worsen and/or spread and cause the complications I went through above. These are just common likely outcomes when a rabbit has a URI, but nothing is a certainty.
If you think your rabbit does have a likely URI, my
opinion as a normal rabbit owner and
non medical person, would be to treat while it's not yet worsened, as you would have a better chance of getting it cleared up more easily. But being your rabbit, the choice is yours to make. You can certainly decide to wait and see if it wasn't what you thought and your rabbit is fine, or if the white discharge shows up again and you'll know for sure at that point.