Nose: air passage blocked from broken nose. (photo)

Trauma to the nose can cause a non-displaced nasal fracture, a displaced nasal fracture, it can fracture the upper lateral cartilages off of the nasal bones, and can cause a deviated nasal septum. All of these issues can block airflow to some degree. After trauma to the nose, it's important to visit an ENT/ facial plastic surgeon to document the extent of the injury. X-rays may be also necessary. Nasal surgery to straighten the external and internal portion of the nose may be required to improve airflow dynamics through the nose. For more information  and many examples, please see the link and the video below

There a variety of reasons to have a blocked nasal passage (nasal obstruction) after a broken nose. Common reasons can include swelling inside the nose, a deviated septum, or deviated nasal bones. After nasal trauma, swelling can be present for several weeks and even up to several months after the injury. I would recommend seeking out a consultation with a board-certified facial plastic surgeon or otolaryngologist to fully evaluate your nose.