It is not at all necessary to undergo general anesthesia to correct a nasal fracture. If it is arecent fracture, within about two weeks, then it could be done either with local anesthesia or alternatively a light sedation. I usually recommend a light sedation for the procedure. If the fracture happened more than a few weeks ago then correcting this is more involved and I would then recommend either sedation or general anesthesia.
Technically, a nasal fracture could be reset without general anesthesia. However, it can be very uncomfortable for patients to have it done in the office and, on occasion, this discomfort can prevent a complete correction. In my practice, I use some tricks to make it much more comfortable in the office, so I do 95% of these under local anesthesia only. However, general anesthesia is still needed in the minority of my patients.Hope you find the solution that works for you.