Septoplasty or Rhinoplasty by an ENT Doctor?

Although there are many qualified ENT surgeons who perform rhinoplasty well, you must be able to chose your surgeon. The individual who you are referring to may be an excellent surgeon and has fantastic surgical outcomes. If that is the case, check out their web site for photos, if they have one, and also photos of similar patients they have performed the surgery on. You can also ask for patient references. These are not always readily available, but, if they have performed enough rhinoplasties, they will have books of photos and plenty of happy clientele willing to share their stories.
Good luck.

This can be a difficult procedure and likely cartilage grafting will be required.  Get a few consults and choose surgeon who does at least 100 (preferably 200) rhinoplasty procedures/year and has been doing so for 10+ years.

Choose a surgeon who specializes in nasal surgery. It is important to realize that not all plastic surgeons, nor all ENT surgeons, routinely perform rhinoplasty in their practices. It is imperative to find one that does. Rhinoplasty takes considerable experience and training to get predictable results. Inquire about what percentage of the doctor's practice is devoted to Rhinoplasty.
Your rhinoplasty surgeon should be Board Certified in either Plastic Surgery or Otolaryngology (Ear, Nose, & Throat Surgery). Not all "cosmetic surgeons" have completed the rigorous training that is required to become Board Certified in either one of these specialities. It is important to find a surgeon who understands both the aesthetic (cosmetic) aspects of nasal surgery as well as the functional aspects.

 See the doctors work and make sure he is experienced and does many noses per year. An ENT or facial plastic surgeon can do a good job if they are good surgeons.

The most concerning part of your question is your statement that you don't get to choose the surgeon. By this, I presume that you are at a teaching facility where a resident or fellow will be performing your procedure (at a reduced fee?)
This does not sound like the kind of case for a surgeon-in-training to be tackling, given that you've had previous surgery in the nose. This is one of those cases where some experience by the surgeon is definitely critical.
All the best,
--DCP