As your vet has diagnosed, it does sound like your cat has an inner ear infection (otitis media/interna)
This can cause a head tilt and falling to one side.
When cats have an ear infection in the outer canal (otitis externa) we usually see symptoms like discharge, itching and a red ear canal. There may be a foul odour.
Sometimes an infection like this can spread to the inner ear, but we can also see inner ear infections without any signs of an outer ear infection.
Inner ear infections can only be diagnosed by looking down the canal with an otoscope to check for bulging of the ear drum (indicating fluid build-up behind it).
Otitis media/interna can lead to irritation of the vestibular apparatus which can lead to episodes of dizziness and vertigo. This problem is treatable with antibiotics given by mouth.
It would usually take 3 days before you could start to see improvement, and a full week before dramatic improvement would be expected.
If the vestibular apparatus inside the inner ear is inflamed, then the eye-flicking and head tilt may be more pronounced. This should improve after about 3 days, though some cats will have a permanent head tilt.
I also want to mention that there are NO human pain killers or fever reducers that you would have at home that are safe to give a cat. Aspirin, acetaminophen (paracetamol) and ibuprofen are all very toxic to cats and should never be given! You can read more about them here:
Your veterinarian would be able to prescribe safe pain killers for your cat, however. You should be able to just phone and ask for some, and might not need to take the cat back in as he has been so recently examined.
If your cat were my patient, I would definitely want to have a close look down inside this ear in the next week. It may be that the ear was too painful and occluded with debris for your vet to be able to examine when your boy was in a couple of days ago. It is really important, however, that the ears be closely inspected to see what is going on in there. He may have a foreign body like a grass awn trapped in the ear canal. The ear will not get better until that is removed, if that is the case!
I hope that this is helpful to you and that your cat starts to feel better soon!
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.