Flying does two things that are relevant to dizziness-- it may induce motion sickness, and it may stimulate the ear through pressure changes. There is a small literature about alternobaric vertigo. In small planes, dizziness may come from either or both mechanisms.
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In most individuals, the sensation of rocking, bobbing, swaying, etc. following a cruise or other passive motion experience is transient. Symptoms lasting up to two weeks is considered within the normal range.
Obstacles like rapid altitude changes, visual disturbances, patterned airport carpets, and passive motion can amplify symptoms. Many people with vestibular dysfunction need accommodations or restrictions to prevent symptoms, attacks, or flare-ups. Having a vestibular disorder should not prevent someone from traveling.