Where do I start with nasal surgery? I have functional as well as aesthetic issues with my nose, where do I start? (photos)

Thanks for sharing your question and photos. You do have clear nasal deformities in your pictures that will need surgical correction to address. Your nasal breathing should significantly improve with a combined septoplasty/rhinoplasty (septorhinoplasty), but some of the other issues that you list, such as chronic migraines and constant nasal drip, can be multifactorial and may not resolve with this surgery. This is something to discuss with your surgeon at your initial consultation, so that they can perform a complete exam and discuss expectations with you.
Insurance companies will typically cover surgery that is performed to improve your nasal breathing. Because part of your issue is related to a crooked nose, straightening this to improve your nasal breathing should improve the external appearance of your nose as well.
To determine your best treatment options, you should schedule consultation with a surgeon who has a great deal of experience with nasal surgery. There are many ENT (Otolaryngology) doctors who are skilled in nasal surgery, but if you are looking for somewhere to start I would seek out a surgeon who has undergone specialized fellowship training in facial plastic surgery and who has particular expertise with rhinoplasty procedures. 
Best wishes,

Thank you for the question and photos.  Your deviation has many causes.  First you have a dislocated septum to the left(notice your left nostril is smaller), which often has a deviation inside the nose.  I feel you should have spreader grafts to stabilize the middle of the nose and osteotomies to bring the nose back to the middle.  I would see an ENT who does either plastics or facial plastics and specializes in rhinoplasty.  

I would recommend an in-person consultation with a rhinoplasty expert.  This can be a plastic surgeon or ENT/facial plastic surgeon.  It appears that you have a left deviation of your entire nose with a C-shaped deformity.  Your caudal septum is dislocated to the left.  Therefore, you will likely need a septoplasty to correct the deviated septum, bilateral spreader grafts positioned in such a way the fills the right sidewall concavity, medial oblique and lateral osteotomies to move the left deviated nasal bones toward the midline, relocation of the caudal septum from the left to the right side of the anterior nasal spine, and a columellar strut graft to support the tip.  These maneuvers should help improve your breathing in addition to improving the appearance.  I would recommend consulting with a surgeon well-versed in rhinoplasty to correct your breathing problems and achieve the natural appearance you desire.  Best of luck!
Ziyad Hammoudeh, MD

To figure out all of your cosmetic and aesthetic needs regarding your nose, make an appointment with a  double board certified ENT/facial plastic surgeon who can handle both the functional and cosmetic components of your nose simultaneously. A deviated septum is fixed with a septoplasty to improve airflow dynamics through the nose. The rhinoplasty is performed for cosmetic purposes to change the shape of the nose. Each one of these procedures can be performed  simultaneously under one anesthesia which allows one recovery period. For  more information about the differences between the two procedures and many before-and-after examples of cosmetic rhinoplasty, please see the video and the link below