I've flown a couple of times with this thing and apart from the effects of general airport chaos and tiredness it did'nt really affect me.
However, your experience will depend entirely upon the underlying cause of your vertigo. Mine is inner ear related and so is (technically)not affected by pressure changes. You say you do not know the cause of your vertigo, but (I could be totally wrong)I seem to remember you saying you had a TMJ problem. From the little I know about this disorder, I think that this can be adversely affected by flying.
You really need to consult the doctors/dentists you have been seeing to discuss the issue of flying with them. I don't know what if any medication you are currently taking, but they may be able to prescribe you new/stronger drugs (vestibular depressants, muscle relaxants, anti-emetics etc) to help you get through the flight. Try to do this sooner rather than later to give yourself time to try them out - you don't want surprise nasty side effects on the day!
Hope this helps a little bit, good luck, xx