Will the Cartilage in Your Nose Heal on Its Own?

It appears you may have a perforated septum.

The nasal septum is a sheet of cartilage and bone that separates the nasal cavity into a right and left side. A hole or perforation can develop in this sheet which allows air to travel abnormally between the passages. Small holes or perforations usually do not cause symptoms. Nasal symptoms from a septal perforation may include bleeding, crusting, pain, or discharge.

Surgery would be required to close the perforation. Only after a comprehensive evaluation by a rhinoplasty or nasal specialist can he/she help determine appropriate options for you.

What pain medicines were you taking and for what?  What do you take now to control the pain.  Did you use other products that were nasl sprays such as afrin.  It sounds like a septal perforation that will surgical correction.

You have a "perforated septum"

To close  it it will require surgery. It will not heal on its own