Yes, rhinoplasty or cosmetic nasal surgery may contribute to breathing problems with the nose.
Nasal congestion may either be immediate or chronic with rhinoplasty / nose job surgery. Most immediate nasal congestion after rhinoplasty surgery is due to normal postoperative swelling. A majority of this internal, as well as external, swelling resolves within a couple weeks. However, it may take a couple months for the final internal swelling to resolve. Some surgeons use cotton nasal packs or silicone splints after surgery. Normal crusting and scabs inside the nose also keep the breathing down after surgery.
Long-term nasal congestion after nose job / rhinoplasty surgery is more of a concern, and due to many, many conditions, some of which may not be due to the original surgery. Fortunately, it is uncommon to have long-term nasal breathing difficulty after rhinoplasty. Allergies, nasal polyps, dust exposure, and sinus problems all cause nasal congestion. These nasal breathing problems can be evaluated by an otolaryngologist and treated accordingly.
Turbinate hypertrophy and deviated septum are common potential causes. These conditions are also usually easily treatable.
Lastly, scarring or major alteration in the structure of the nose after rhinoplasty surgery can contribute to breathing problems. Fortunately, this is usually the least common cause of breathing issues following surgery.
Speak to a facial plastic surgeon, who specialized in both the inside and outside of the nose, to perform a comprehensive examination and help guide your treatment plan.