My nose feels numb too after anesthesia. Is that normal?

Yes, it is a normal reaction, so there is no need to worry. When the upper front teeth or premolars are anesthetized, the nerve involved also supplies sensation beside the nose and around the lip, so the nose, lip, and cheek can feel numb together. The anesthesia usually wears off within 2 to 3 hours. However, if sensation has not returned a day later or the numbness continues, there is a rare possibility of nerve damage, so please come in to have it checked.