Poor bunny
Definitely sounds like snuffles! Some vets still start with the antibiotic Baytril and it does work on occasion, although many vets now use Septrin and find that to be more effective. It does need to be a relatively long course of antibiotics, otherwise it will be leaving the more resistant bacteria behind.
If your bun is particularly snotty it's probably worth asking for some bisolvon powder as well, this thins the mucus so it is easier for your bun to breathe. I got some bisolvon for my snotty little one yesterday and her breathing is much easier this morning.
Don't know what others think, but I would be inclined to leave your bunnies together - one of the trigger factors for snuffles is stress, so changing the normal environment including a companion, can make it much worse. They all carry the bacteria naturally anyway so it's probably too late to do anything about it for the other one. Sometimes the other bun in a pair will also become snuffly, but often they don't. My other bun in the pair is absolutely fine he has never developed snuffles despite living with a snuffly girl since last November!
Good luck, let us know how you get on at the vets.