Currently-used anesthetics have an approximately 1/10,000 to 1/100,000 chance of severe and fatal allergies. In addition, patients are monitored by instruments throughout the entire surgical procedure as well as in the recovery room. Therefore, if an allergy does occur, it can be immediately discovered and treated to avoid further injury.
Other minor allergies, such as skin rashes, gradually disappear after the end of the anesthetic’s action. The doctor will note this and avoid using such anesthetics in future as much as possible.