What kind of doctor would I go to for deviated septum and cosmetic repairs?

First and foremost, you need to go to a physician that specializes in cosmetic and functional nasal surgery.  Experience in performing these procedures is the key to your best chance for having a great result.   That being said, a facial plastic surgeon is an excellent choice.  Facial plastic surgeons provide a unique skill set in that they are trained in both Otolaryngology ("ENT") and facial plastic surgery.  This specialized training gives facial plastic surgeons excellent knowledge and expertise in dealing with both cosmetic and functional issues regarding the nose.  I suggest in person consultation with a facial plastic surgeon specializing in rhinoplasty to discuss your options.  I have provided a link below.  Good Luck!

... until you've checked the doctor out thoroughly. All other things being equal, an ENT will have a better idea of what to do with your septum, but there are many plastic surgeons who can handle the septum great as well.And things are never equal. Very few plastic surgeons and ENTs can do an excellent job with a rhinoplasty.Be sure to read the section in my "Web reference" link on how to stay out of trouble while searching for a rhinoplasty surgeon. You should only have surgery if you are able to make yourself very confident in your surgeon's skills.
I usually make computer morphs when I'm answering a RealSelf question, to show the changes that are possible for your nose with a rhinoplasty. For example see this page:FacialSurgery.com/RealSelf/RealSelf_Morphs.html
But of course you didn't post any photos. At the *very* bottom of the Web reference page is a link to instructions on taking photos that are comprehensive and useful for online consultations like this, in case you'd like a more complete evaluation.

It appears that our academy has not done a good job of public education.  You need to see a facial plastic surgeon.  This is an ENT with extra training in facial plastic surgery.  We are double board certified in ENT and facial plastic surgery.  Most facial plastic surgeons specialize in cosmetic and functional nasal surgery.  

 A double board certified ENT/ facial plastic surgeon should be able to handle treating both a deviated septum and cosmetic repairs for the nose.   Look at your surgeon's before and after photo gallery for rhinoplasty to make sure it is it is extensive, since rhinoplasty is much more difficult than the septoplasty component. 

First you need to know that airway obstruction could be caused by many things among which is deviated nasal septum. May need turbinate work, may need support of the nasal valve to get the improvement in airway obstruction.Both specialties, ENT and plastic Surgeons can and are qualified to do both.The important part is to choose the right surgeon with experience in both airway obstruction and the cosmetic work needed. For that you need an in person examination and proper diagnosis and choose the doctor or specialist that you trust and can work with.