Yes, nasal trauma can certainly create a bony irregularity in the nose, creating a higher bridge. The nasal bones can also shift to one side or the other, causing the nose to appear C-shaped on front view. This can cause deviation of your septum and narrowing of your internal valves, both of which may affect your ability to breathe. Severe trauma can also cause a fracture of the septum or a septal hematoma, a collection of blood in the septum. After any significant nasal trauma, the septum should be evaluated to rule out the possibility of a blood collection, as this can be serious if untreated.
If it has been more than a few weeks since your injury, a reconstructive rhinoplasty (nasal reconstruction) could be an option, to restore the appearance of your nose.
Best regards,
Dr. Mehta