Sorry to hear that you broke your nose, and even more sorry to hear that you now have nasal obstructive symptoms. Let me first say that nothing I can tell you in a forum setting can replace a visit to an ENTs office. There are multiple different reasons for nasal obstruction. In general you can think of things as being either a fixed or rigid obstruction (like scar tissue, nasal polyps, deviated septum, turbinate hypertrophy, etc...) or dynamic obstruction (i.e. obstruction that worsens with breathing such as collapse of the lateral nasal walls with inspiration).
It is impossible to tell exactly what is going on in your case without being able to take a good history, and examine your nose. However it does sound like your doctor
is starting with an appropriate step to help improve your nasal obstruction by putting you on what I presume is a nasal steroid. The steroid won't actually shrink the cartilage in your nose, as that is a rigid structure, but it will decongest some of the erectile tissue that is within your nose which may improve your breathing. With your history of nasal trauma, I would definitely recommend being evaluated by an ENT if you continue to have nasal obstructive symptoms despite treatment with a nasal steroid spray for at least a month (they can take a long time to work). Hope this helps.