It’s a matter of working with your dentist and dental hygienist to get you as comfortable as possible.
I have trouble lying on my back, and especially tipping back past neutral. So, my hygienist figured out how to clean my teeth with my head supported on a pillow and basically staying as upright as I could. It was a bit awkward for her at first and we had a good laugh as she tried to figure out how to make it all work, but she managed just fine.
For dental work (fillings, crowns) I have managed to be tipped back as most of the work was done with my head turned to the side, which works okay for me.
You might still get dizzy, so make sure you have a ride home; don’t try to drive yourself.
If it gets too frightening for you, you might need to go to a dentist who uses “conscious oral sedation” to keep your vestibular system as calm as possible.