Will septal mucosa regrow? I do not have a hole in my septum yet, and am hoping the mucosa will regrow and I can avoid surgery.

Cocaine is a powerful vasoconstrictor which damages the blood supply to the nasal septal mucosa, which in turn destroys the blood supply to the underlying nasal septal cartilage creating a nasal septal perforation. Unfortunately, you describe a circular white spot on your septum which sounds like exposed nasal septal cartilage. It may be too late to avoid going on to complete septal perforation at this point, even if you have stopped using cocaine entirely. Application of ointments, lubricants and saline sprays may promote mucosal health provided there is no nasal irritation or infection. Search for a specialist in Facial Plastic Surgery for and examination and recommendations. Please do not tempt your fate by returning to your former habit. Wishing and hoping for a good outcome for you. 

On ceasing the habit the white thin scar of the septum will improve.Keep the nose well lubricated with triple antibiotic and dont use afrin or other nose drops ever.

Perforations are common in people who use cocaine so it will not be unexpected if you end up with a septal perforation.  The important thing is to keep the area moist for now with saline (Ocean nasal or Ayr nasal gel are good).  If a perforation does develop than a complex reconstruction with a septomucosal flap with be necessary for repair.  I would recommend someone who does a lot of this type of procedure to do this for you.The most important thing is to stop any further injury to the nasal cavity.