Septoplasty or Rhinoplasty by an ENT Doctor?

 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