Changes in air pressure during flying can cause ear-drum pain and perforation, vertigo, and hearing loss.
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The appearance of dizziness or vertigo during or at the end of a journey is a common phenomenon. So common that almost everyone can report an incident of someone in their environment with such sensitivity.
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.
Attacks of vertigo can develop suddenly and last for a few seconds, or they may last much longer. If you have severe vertigo, your symptoms may be constant and last for several days, making normal life very difficult.