Dorso-columellar augmentation and nostril narrowing is need to help change the shape of your nose to more of what you want. Whether the augmentation is done by an implant or cartilage grafts is open to debate although at your young age I would strongly consider cartilage grafting for more assured complication-free long-term result.
You can still maintain a natural, ethnically appropriate nasal appearance while improving the areas of your concern regarding the upturned shape and width of your alar base and nostrils. Perhaps your surgeon was referring to the width of your nasal bones and not the alae/nostrils. In my view, your nose is too wide. To improve the upturned position and width of your nostrils, you will require techniques to lengthen nose and have an alar base reduction performed. This can be done with cartilage grafts and surgical soft tissue modifications. Of course, this should be balanced with any changes you wish to make to your profile or overall width of the nasal bones. Hope this answer helps.