How to heal nose cartilage?

It sounds like you saw a doctor for suturing the injured area, so if that doctor was a plastic surgeon, you should return there for advice.  If not, then Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 

I am not aware of any medications or vitamins to assist with cartilage healing. There are a few options, however, to improve the appearance of the scar, which include topical medications, injectable medications and/or laser and surgical procedures.  For your information, nasal ala actually has more skin and fibrofatty tissue rather than cartilage, so it may be that your cartilage was not involved in the laceration- just a guess. If you are concerned or unsatisfied with the appearance of your scar, it is better to consult a facial plastic surgeon to address this in person. 

Despite the claims of multiple supplements on radio, print and TV, there is no good evidence of any superior healing I am aware of with supplement. Eat well, don't smoke and keep your head elevated. There is a possibility of some further surgery required  if a deformity, as a part of healing, occurs.All the best,Talmage Raine MD