Nasal Base Narrowing. The narrowest part of the nasal airway is the internal nasal valve, located about 2 cm into the nose. This may be narrowed by osteotomies or hump reductions that weaken the nasal sidewalls, but not by nostril reduction. That is not to say that nostril reduction cannot be overdone. Choose a surgeon with experience in this maneuver specifically who can discuss you options with you.
Fine. If the procedure is performed correctly, the breathing should be good or even improved. The airway must be maintained, the nasal vault must be intact with good support. The nasal base modification should never comprise the airway.
Rhinoplasty. A well-performed rhinoplasty should not only make the nose look better but it should also maintain or enhance the nose's function (breathing). Seek a consultation with a board certified facial plastic or plastic surgeon who performs rhinoplasty frequently.