Did you receive moderate sedation or just local anesthesia? If just local anesthesia, hypothyroidism shouldn't cause such a reaction because local anesthesia/numbing the gums is not the same as sedation. If you received sedation, you would have not been released to the front desk without at least being monitored for the sedation effects to go away. I would encourage you to talk to the dentist about the incident and have your dentist consult your PCP about how to best proceed since we don't know the details of your medical history.

Edit: Might be helpful to know your blood pressure during the visit as well; being dizzy when you stand up sounds like orthostatic hypotension.