I would say not to use essential oils, especially not in the ear. Some can cause ototoxicity and some are not safe if ingested. If it’s an infection, then antibiotics should do the trick. The vet may also recommend an ear wash if necessary. There are dog/cat ones that can be used, but you have to be careful since rabbits are prone to having adverse reactions when it come to their ears. So yes, definitely make an appointment.
My only experience with this is an ear infection that migrated from the sinuses. My Wooly has chronic sinus problems and sometimes bacteria builds up. Everything is connected in there, so infection can spread from the sinuses to the ear. He has never had true head tilt, but he will hold his ear funny if he’s having an issue. He has, however, had mild facial paralysis which can occur with ear infections. We have experimented with different oral antibiotics and ear washes. But his case isn’t typical. There’s no reason to think your bun won’t be just fine after a single course of antibiotics.