How Long After Braces Can I Get Rhinoplasty?

There should not be any reason that you could not undergo rhinoplasty after getting braces on. First, you should check with both your orthodontist and rhinoplasty surgeon to see if they have any concerns.
If you experience any pain with you braces, avoid taking any aspirin, aspirin-containing products, or ibuprofen for two weeks prior to your rhinoplasty as these medications can thin the blood and make you bleed more freely.

I would simply tell the dentist/orthodontist to be a little careful when working around the nose for the first few weeks after surgery. A bump to the nose could be painful, but it would be unlikely to harm it unless something exceptionally rough was done during one's dental visits.
Likewise, a rhinoplasty shouldn't interfere with anything the orthodontist would need to do unless it involved cramming a big tray or something in one's mouth where the top of the tray under the upper lip would put pressure on the base of the columella.
--DCP

There should be no conflict with having a rhinoplasty procedure shortly after have braces placed. I would recommend a waiting period of a week or so to allow the inflammatory stage that occurs with the placement of braces to subside. Remember to stay away from anti inflammatory medications like Advil and Motrin for one week prior to surgery.