When you say broken, it might be good to mention that there are actually no bones in the nasal tip. The nasal tip is made up of cartilages and your trauma to the nose could have caused the cartilages to be damaged. The drooping may have been caused by some of the caritlage loses its connections from elements that are higher up on the nose. The bulbous change could be from scar tissue. All of these changes though require quite a lot of force, so you must have hit your nose pretty hard. These changes can all be improved for you through rhinoplasty (nose job, rinoplasty, nose plastic surgery, nose cosmetic surgery, nose shaping, nose reshaping) and it will essentially require tip work and very likely no treatment to your nasal bones.
One question is whether you have closely looked at the pictures of yourself long before. Sometimes people notice things more after an event and attribute it to the event when it was really has been happening for a long time. This is just a thought though and all this could be from the trauma.
Hope that helps!