No b/c your asleep. Most of the time in rhinoplasty, the patient is sedated or asleep-- therefore the patient will not experience pain during the injections.
Asleep. Usually you are sedated or asleep for rhinoplasty so you do not feel the shots. I would not suggest rhinoplasty under local anesthesia.
Minimal discomfort. Rhinoplasty can be performed with general anesthesia or local anesthesia combined with conscious sedation ("twilight sleep.") either way, the injections into the nose are not significantly uncomfortable. Discuss this issue with your surgeon to ensure that your rhinoplasty is as comfortable for you as possible.
Sedation. Usually you are sedated or asleep before the surgeon injects the nose for rhinoplasty. Doing the procedure under just local is very rare now. If sedated or asleep you will not feel a thing!
No. If you have a general anesthetic, you will be completely asleep prior to any injections. If you plan to have conscious sedation, an anesthesiologist will be able to sedate you deeply enough during the injection that you should have no pain experience.