Can you say embarassing when being put to sleep at a dentist's office?

Not, if needed. Some patients are very dental phobic. It's not any fault of their own that they're this way. Some patients require inhalational, conscious, oral, intravenous, and some even general sedation in order to have their dental work done. I don't think that's anything to be embarrassed about. That's just the way it is for some folks.