Hi,
Do you mean http://www.yogajournal.com/practice/175# this asana?
Are you breathing slowly and fully while you are doing it? Not breathing properly will make you dizzy.
This asana also changes the pressure in the fluid in the spinal column and around the brain as well as the head hanging upside down this can make you dizzy if not accustomed to doing the asana.
Are you doing the asana correctly…without force or strain?
Are you working with a properly qualified teacher who can watch you practice and give advice/correction?
Take it slowly, do not strain and gradually build up the time you spend in the asana so that you do not get dizzy.
If worried about inner ears…go see a doctor.