Can a rhinoplasty cause breathing problems?

If you're having nasal blockage after your rhinoplasty, you should have a consultation with a board-certified ENT or facial plastic surgeon to determine the cause. If your breathing improves with a topical decongestant spray, you might benefit from an in-office turbinate-reduction procedure.
I am not aware of any chronic illnesses caused by rhinoplasty.
Best regards.

 They can however have problems which can be caused by the surgery as far as obstruction is concerned. See an experienced rhinoplasty surgeon to evaluate the cause.

In the healing period after rhinoplasty congestion can occur as the internal and external swelling diminishes. After a few months this should improve. persistent obstruction may be due to a narrowing of the airway while breathing in, known as valve collapse. This is a common problem if not anticipated before the surgery. You should consult an experienced facial plastic surgeon to see if this or other problems exist.

Mel24 Brea,
Yes, rhinoplasty or cosmetic nasal surgery may contribute to breathing problems with the nose.
Nasal congestion may either be immediate or chronic. 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 plastic surgeon or 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.

Airway obstruction after rhinoplasty is certainly possible. Two years after surgery the quality of nasal breathing will not improve. You have been patient, waiting for the post-operative swelling to resolve. Schedule consulation with your original surgeon or another physician.