Can a permanent bump form on the bridge of nose after a hard hit?

It is possible to develop a bump on your nose after trauma. However, it will take some time to determine whether this is permanent or temporary. There is something called a bony callus that can form and be permanent but most likely the majority of the bump you notice is more related to edema which may resolve. I would wait until six weeks after the injury to further assess this. If persistent, I would recommend you follow up with an experienced rhinoplasty surgeon Board Certified in either Facial Plastcs or Plastic Surgery. 

Injuring your nose can result in either temporary swelling or even a permanent bump depending on the degree of trauma.  Typically swelling may last 1-3 months.  An x-ray may help  determine if a fracture occurred, or if it is simply swelling from bleeding under the skin.  It may be wise to see a physician to document the injury, in the event that a surgical correction is necessary

it is entirely possible you fractured your nose. Nasal trauma can fracture the nasal bones, which are quite delicate. This can cause both functional and cosmetic deformities to the nose, which will need to be addressed. The only way to know is to have a physical examination. Usually X-rays are unnecessary. 

Trauma to the nose can cause a displaced nasal fracture, a non-displaced nasal fracture, dislocation of the upper lateral cartilages off of the nasal bones, and twisting of nasal tip cartilages along with a deviated septum. Trauma to the bridge of the nose can also cause a callus formation which creates even larger bump at the bony cartilaginous junction. It is important to seek out examination by an ENT /facial plastic surgeon to evaluate and document the extent of the injury along with x-rays.  If the bump is still present after three months, surgery may be needed to remove it. Digital computer imaging would be helpful to understand what can be accomplished with a closed rhinoplasty procedure. For more information and many examples of dorsal hump removal, please see the link and the video  below

Yes, it is possible to get a permanent bump on your nose after a fall.  This can occur from the blood there (hematoma) to broken bones and other issues as well.  On the other hand it is not only too early to tell, but you noted that it has been changing.  Swelling in the nose also takes a long time to resolve.  In the end I would recommend waiting and watching and I you want to do anything at all, then occasionally massage the area which may help any scar tissue in that area.  Good luckGarrett A. Wirth, MD, MS, FACSWirth Plastic Surgery