Is it possible that i have an allergic reaction to the dentist's numbing medicine?

Unusual: Allergic reactions to local anethetics is distinctly unusual - some argue that it may not exist. If one has had a reaction to a local numbing medicine then an evaluation is needed before using that medication again.

Unlikely: What reaction did you have? There are a lot of reactions to dental work that are completely normal. There are also many more likely causes of abnormal reactions, including allergies to other substances, like latex. A list of your symptoms/reactions would help. However an allergist would be able to pinpoint what is the problem definitively.