Rhinoplasty performed to correct an anatomical abnormality that obstructs breathing should be covered by insurance. Unless your current health care insurance excludes pre-existant condoitions, you should be OK.
Your doctor will have to document your breathing difficulty with notes and possibly photographs.
I would check with your insurance company about their requirements before your consult with a doctor. It would be best if your primary care doctor diagnosed the problem and referred you to a surgeon for treatment.
Be sure to request a plastic surgeon as many ENT surgeons will only correct the airway and not bother with the look of the nose.