ENT Doctor or Plastic Surgeon to Repair Broken Nose?

This is the type of advice that would require photos and or a full examination. With a complicated issue such as this one, and since it is a revision, it may be best to seek out a revision rhinoplasty specialist and/or a facial plastic surgeon. In particular, facial plastic surgeons are a great option since they have the functional aspect covered from ent training and the aesthetic vision due to training in facial plastic surgery.
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Having had a previous rhinoplasty introduces an additional degree of difficulty in repairing your daughter's nose. I would recommend either a facial plastic surgeon who has background in ENT surgery or a plastic surgeon who does a lot of rhinoplasties. Also, I would see someone who has done a fair number of revision surgeries due to the added intricacies involved in repairing a nose that has been previiously operated on. I hope this information helps.

I would focus on a Facial Plastic Surgeon (Otolaryngology background) or Plastic Surgeon who is experienced in Rhinoplasty surgery. Both specialties are trained to perform this type of surgery, but only some individuals within each specialty take a special interest in it and/or obtain consistently good results.

Since your daughter had previous nasal surgery, she should consult an experienced, board-certified Rhinoplasty surgeon with many favorable photos. Since the injury was yesterday, she should be seen within the next week or so, as she may only require a closed reduction of her fracture with local anesthetic in the office.
I hope this is helpful for you.

 The specialty is of less concern than the ability and experience of the surgeon. Look at real patients the surgeon has done and speak with them.

Your best bet in the setting of a nasal fracture after a rhinoplasty is seeking treatment from a surgeon who focuses the majority of their practice on the nose. There are both facial plastic surgeons (ENT) and plastic surgeons who would fall into this category.
Your research should be geared toward the ability to correct problems from previous rhinoplasty surgery (revision rhinoplasty), and ability to correct berathing problems.
Insurance may cover certain aspects of the procedures required to restore the nose to its previous condition. There are certain parts of the procedure that will be considered cosmetic. The best way to know what your insurance will cover is to find a surgeon who can handle the problems, then get codes for diagnosis and for proposed surgical procedures that can be submitted to your insurance company to deterimine coverage in your particular case.
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There are many superb ENT trained Facial Plastic Surgeons and many superb Plastic Surgeons who understand the nose. However, if you have had a prior rhinoplasty and now broke your nose, you want the most skilled person you can find who can address your nose inside and out. Seek out a specialist who devotes the majority of their practice to the nose and can treat both the cosmetic and functional aspects of the nose.

This is an excellent question, thank you for posting. There are several things to take into consideration when selecting a surgeon. It is important that you verify that your surgeon is Board Certified in either ENT or Plastic Surgery. Both these specialties are well equipped to handle your specific problem. It will be beneficial to select a surgeon who has expertise in revision rhinoplasties as well as someone you are comfortable with.

It will be necessary for the surgeon you select to first have an in-person consult along with reviewing the CT. This will help identify your fractures as well as any associated sinus issues. In addition it would help to get the operative report of the previous surgery. 

Facial plastic surgeons, general plastic surgeons, ear, nose and throat doctors are all trained and should be capable of performing rhinoplasty surgery. The question is not the specialty but the individual surgeon. It would serve you well to find a surgeon who is very experienced in performing rhinoplasty and maintains a reputation for achieving consistently good results.
You have to discuss financial matters and insurance with the surgeons with whom you consult. Cost and coverage are very important, but obtaining good results is even more important.

Any board certified ENT or plastic surgeon with an interest in rhinoplasty surgery will be a good choice. But you have to do your research and make sure the surgeon can show you before and after photos.
Insurance will only cover the portion of the surgery which is medically necessary. Making the nose more refined is considered cosmetic and will not be covered.