If you're allergic to anesthesia and want to have a rhinoplasty, is it possible?

Rather than trying to see if a rhinoplasty can be done under local anesthesia, the first question would be to determine what this 'allergy' to anesthesia was. Nobody is truly allergic to anesthetic drugs per se but one could have had an atypical response to them that can be avoided he next time. You would have to describe what problems you had with your general anesthetic to determine the true nature of the reaction.  

Are you talking about local anesthetics or drugs that are used for sedation or general anesthesia. After determining what you're allergic to by reviewing your previous history talk to your surgeon and their MD anesthesiologist to review your options. I'm sure there are drugs available so you can have a pleasant experience.