D.W.
It's completely possible to be allergic. Anesthesia is the most difficult specialty in medicine some would argue because you're administering things (usually into the central nervous system) that can have varying effects. A friend is an anesthesiologist and basically says they bring people to the brink of death and back for a living.
I'm really surprised they administered it a second time after having the reaction the first time. Have you asked them to send the medical records to your primary care physician to be in your permanent medical files?
Have you mentioned this to your primary care physician? If not, you should call them immediately and see how they want to move forward. They may refer you to a specialist to verify the allergy to make sure you're not administered the same ingredients again.
Because of one of my chemo drugs, bleomycin, I have to make anyone administering anesthesia aware so they adjust doses. Otherwise, I could die. I probably should wear a medic alert bracelet in the event I'm in an accident.
Good luck.
http://www.drugs.com/pro/novocain.html