No, the injection was the right treatment if it is ear mites and not an ear infection causing the excess scratching. Baby oil is a home remedy which has to be applied every day and doesn't always work. The injection was likely ivermectin, which is the correct treatment for mites in rabbits. And yes, it does have to be given two more times, two weeks apart.
MediRabbit (ear mites in rabbits)
Of course the better option in my opinion, is to use spot on Revolution(selamectin). Sometimes one treatment is enough, so doesn't necessarily need to be reapplied, but can be to be safe. Instead of going back for two more injections, I would ask your vet if you could just pick up some Revolution for the remaining treatment. Revolution is a prescription antiparasitic. It's just applied topically between the shoulder blades, and you can do that yourself at home. You should be able to just go in and pick up a tube from your vet and not even have to bring your bun back. If you want an even cheaper option, tell your vet you would like to buy it online or find a local pharmacy that carries pet meds to get it from, and the place can call your vet for approval. Vet offices usually triple med prices, so much more expensive to buy from them. Or stick with the injections if that proves cheaper.
It also is possible to buy injectable ivermectin otc online. I've given it orally in the past when necessary, ,but it's better to only do that if experienced and comfortable calculating dosages and administering medications, as an overdose is toxic with no reversal med. The UK has ivermectin available as Xeno 450 spot on for rabbits, which I really wish we had available here in the US. It would make it so much easier for rabbit owners here.
No special cleaning. Just throw out old litter and hay, and wash anything else you can after your rabbit has been given the med.
