Can an Injury Cause a Dorsal Hump to Form on the Nose?

Yes, the hump can be created as result of calcium deposit and bony growth in the area of trauma. Sometimes septal deviation, nasal valve
collapse or turbinate hypertrophy can create congestion or difficulty
breathing and these conditions can also be corrected by specific
procedures.
I would recommend that you would be seen by a nose specialist with passion for rhinoplasty.Best wishes,Dr Sajjadian, Triple Board Certified Plastic Surgeon
DrSajjadian.com

A dorsal hump can arise from overgrowth of bone formed in response to a healing fracture.This trauma may have also caused your deviated septum. Seek advice from a board certified Plastic or ENT surgeon

A prior nasal fracture could cause a dorsal hump to form or worsen an existing hump. However, the hump may have just developed as your nasal bones matured.  It sounds like you would benefit from a septoplasty to correct your deviated septum, turbinate reduction and a rhinoplasty to remove the hump and refine the shape of your nose. 

You may have broken your nose at the time of one of your injuries.  This will have caused the bones or the cartilages in your nose to become deviated and one may have outwardly protruded giving you this subtle hump on your dorsum.  A proper physical examination will help determine if a deviation has occurred.

You are correct. The injuries to your nasal bridge are the cause of the problem. The breathing issues are also related to the trauma but may have an underlying allergic cause with the turbinate enlargement. Surgical correction would be helpful for your appearance and function too. Best, Dr. G.