Can a person have a reaction to novicaine?

Yes, there could be side effects to Novocain such as:

an allergic reaction (difficulty breathing; closing of the throat; swelling of the lips, tongue, or face; or hives);

chest pain or slow or irregular heartbeats;

dizziness or drowsiness;

anxiety or restlessness;

nausea or vomiting; or

trembling, shaking, or seizures (convulsions).

If you have any reactions you should probably contact your doctor.