Can i have an allergic reaction to the dentist's numbing medicine?

Yes, but unlikely.: The anesthetics used in dentistry now, have a very low likelihood of causing an allergic reaction. If you have bruising or inflammation in the area of the injection, this is not uncommon. Just wait it out a few days and the bruising and soreness will resolve.

Possible: The most likely candidate for an allergen is the preservative used for the vasoconstrictor in dental anesthetic. Anesthetics without the vasoconstrictor and therefore also without the preservative are available. You may have had a non-allergic response though so tell your dentist so you can figure out exactly what is going on. If it is a true allergy, you need to know and avoid the allergen always.

Unlikely: Local anesthetic allergy is extremely rare. Most of the side effects is from the Epinephrine mixed in it to extend the effectiveness. The short answer is yes , almost any medication cause cause problem for some but in the case of local anesthetics the answer would be unlikely. If you are allergic to latex, make sure your dentist is aware of it.