Can a broken nose be repaired years after incident?

It usually is possible to treat the effects of prior nasal injury (fracture or other trauma) years after the incident. There are many aspects to rhinoplasty surgery including the issues you're having with breathing that should be evaluated. Your surgeon would ultimately need to examine your nose, including the inside to assess what is going on and what can be done to repair the damage.You can check out my web reference link below to read more about nasal hump removal and to see some before and after photos of other rhinoplasty patients.

Although pictures or an exam would be helpful, you would probably benefit from rhinoplasty.     Find a board certified plastic surgeon who performs hundreds
of rhinoplasties and rhinoplasty revisions each year. Then look at the
plastic surgeon's website before and after photo galleries to get a
sense of who can deliver the results. Kenneth Hughes, MD Los Angeles, CA

Fractured nose repair can be done years later based on my 35 years of doing this. Select a very experienced rhinoplasty surgeon who does natural noses. 

If you are having difficulty breathing through your nose, your insurance company may cover the cost to improve your functional problems.  However, insurance companies most likely won't cover any costs to improve the appearance of your nose even if it is related to a broken nose.  I recommend you see a plastic surgeon for consultation to examine your nose and determine what improvements can be made.

Sorry to hear about your dodge ball incident I always hated that game.  Anyway based on the description provided it sounds like a rhinoplasty procedure would help all of the issues you are dealing with.  Contact a local plastic surgeon with your parents to discuss your concerns.