m not sure about bacterial infections (for which antibiotics are given), but viruses can affect the
inner ear and cause dizziness. Usually the
symptoms clear up in a matter of days or weeks, occasionally longer. If they don't improve, see an ENT, preferably an inner-ear specialist (otologist or neuro-otologist).
As for activity, take it slow, but do remain active. The key to getting over a viral inner-ear infection is to stay active once the acute phase passes.