Rhinoplasty Under Local Anesthesia?

Rhinoplasty can be performed under local anesthesia without complication. The real issue is whether this is the safest choice for anesthesia and whether your surgeon is compromising your result by minimizing the type of anesthesia. I generally prefer to perform the surgery under general anesthesia as I prefer to meticulously sculpt the nose during rhinoplasty.

Local anesthesia may initially sound like a good idea for Rhinoplasty, but it's not necessarily the safest, nor the easiest circumstance for you or for the surgeon. As other posters have noted, anesthetic techniques are very safe in healthy patients. I routinely use General Anesthesia for Rhinoplasty (usually with LMA).
As far as evaluating for your nose, I would recommend a consultation with a local Rhinoplasty surgeon; your picture is not adequate to give any meaningful advice. New York City has many qualified surgeons who match this description.