How Can I Tell if my Nose is Just Badly Bruised?

It is often difficult for patients to examine and diagnose nasal injuries properly. In most cases, patients should see a physician for a formal exam and diagnosis. In some cases, imaging might be needed, but this is not something I routinely recommend for isolated nasal injuries. 
Ideally, the exam should be performed by a specialist in rhinoplasty such as a facial plastic surgeon. Be sure to see an expert.
Best,

  It is best have an examination by a ENT or  facial plastic surgeon to determine if there has been a fracture of the nose bones or septum, and to make sure that there is not a septal hematoma. Also important to make sure the upper lateral cartilages had not been fractured off the nasal bones. X-rays can also be helpful.

Point tenderness and a new bump on the bridge are signs that you could have a nasal fracture. An X-ray or CT scan would be able to identify a fracture, although it is probably not necessary to get one. The decision on whether or not you nee treatment is made based on presence of new nasal obstruction or new nasal deformity. I would recommend you be seen by a surgeon who is familiar with nasal injuries and their treatment (facial plastics,ENT, or plastic surgeon).