A couple years ago I developed a “wart like” spot on the cartilage inside my nose between my nostrils..

It grew large enough that it was irritating. Instead of seeing a doctor, I kept trying to remove it myself. This past April It finally broke loose. When it was removed it appeared “woody” and my nose bled a lot. After a few days I realized that the cartilage between the nostril had a hole where the “wart” had been and the cartilage is loose. My nose does not hurt, but the cartilage near the hole remains tender. Should I see a doctor for “repair” of this cartilage?