Could you try human at-home exercises on the rabbit to help with inner-ear balance/vertigo? I'm not sure how effective it will be, or even possible, but it might be worth a try.
Antibiotics in the ear cannot hurt too much if done correctly. For the possibility of a tick/mite:
> The tick would cause rashes/swelling and would be generally apparent, the area would be itchy, and the rabbit would show signs of that.
> Mites are so small that it is basically impossible for them to, alone, have an effect on the ear canal. Additionally, they basically just eat ear wax and also make it itchy. However, they can cause infection. If you can stick JUST the end of a cotton swab (make it wet, make sure to get off any loose cotton, and stick in ONLY the cotton part, not more of the stick, and twirl it) and see any black/dark brown debris, that is the sign of mites. There is no way to get rid of in-ear mites without a vet to my knowledge, but should treat as if infection. If you end up finding over-the-counter stuff for treating mites in ears after confirming your rabbit does have mites, inform us!
What is most probable as the cause is infection, or the rabbit was born with a balance issue related to the ear and skull, and it has become apparent now if it is still growing. That is, if all of what
@NotabitaiI said wasn't applicable, which had good concerns.
That, or your rabbit is being extremely silly in method to lie down, but that doesn't sound like the case if it tries to get back up.
