I am not sure, but in some states, I think the dentist can give you something or you can go to a doctor, prior to the dentist, who will give you a prescription for a single valium or some other med to stop this. If you do go to a doctor prior and he gives you a med, you need to discuss it with the dentist as the med he administers to numb you can cause the other med to be immediately be processed out of your system.
I have Schizophrenia and within 20 minutes of being given the shot by the dentist, my antipsychotic med gets processed out of my body and for the next several hours until the dentist's shot wears off, I have to suffer full blown Schizophrenia.
I think many, many people feel what you do when you go to the dentist and that is why so many people wait untill their teeth rot out before they go
Also you need to tell the dentist this, as you may be allergic to something that he is giving you or putting in your mouth, as it may be triggering an asthma attack.