The nose you describe is typical of many asian patients. However, many different patients of varied ethnicities have issues like the ones you describe. African american, Latin American, Filipino, and many other ethnicities can have this type of architecture.
A 'narrow' nose is one which has deep shadows along the sides of the nose and a nice highlight in the center. In order to provide this, the nose has to have a certain height. If the nose is too flat, then it gets washed out and does not have the contrast to appear narrow.
Typically, cartilage grafts and, occasionally, silicone grafts, are used to establish this height. Which one you would need depends on your individual anatomy and personal goals. This is true for both the tip and the dorsum (upper 2/3 of the nose).
Hope it helps you feel more confident that you can achieve the look you are seeking.
Best of luck.
A representative before and after has been posted to my profile. Feel free to look at it. Hope it is helpful.