How long does it takes to heal the cartilage and columella? (Photos)

You have to give yourself some more healing time.  Your nose and surrounding areas are going to be swollen for a while and you should be consulting the surgeon that performed the procedure. However, give yourself some time before going back in so some of it can subside. It can take up to a year for final results.
Sincerely,
Philip J. Miller, MD, FACS Double Board Certified Facial Plastic Surgeon

Thank you for your question and photos! Without before photos it is difficult to assess your post-op photos. However, being only one month post-op it is common to still have a lot of swelling. It can take up to a year to see the final result from a rhinoplasty. I recommend giving your nose more time to heal and keeping in contact with your surgeon. It is important to express concerns so that you both can be on the same page.
Best of luck, 
Dr. Kian

Hello and thank you for your question and sharing your photos. It is expected to have prolonged swelling after rhinoplasty.  I would wait several more weeks to months. Follow up closely with your surgeon. You might benefit from a revision surgery down the line, but it's too early to at this point. Best,

Hello and thanks for your question.  In general, it takes about 6 weeks for cartilage and bone modifications in rhinoplasty to heal and be stable.  Skin and mucosal incisions are healed and stable more quickly, although scar maturation goes on for about a year or so.  In terms of swelling, about 2/3 to 3/4 of the swelling of the nasal tip is gone by about 6 weeks postop, and the residual swelling gradually resolves over the first postop year.  Keep in contact with your surgeon.  If needed, a revision rhinoplasty can be done after about a year.  All the best.

I would usually default to the surgeon and say trust his/her instincts and opinion, however, in truth, the columellar skin was not well approximated here. The nostrils are asymmetric and the skin doesn't line up.
It would be worth revisiting them to express your displeasure. This can commonly be addressed in a revision procedure a few months out.