Is It Possible to Fix Wide, Pig-like Nose?

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.

It’s not unusual for Asian patients to have many of the nasal characteristics that you describe. Asian patients often have rounded nostrils, flat nasal bridges, short nasal length, and an upward tilt of the nasal tip. When these anatomic findings are combined they make Asian rhinoplasty one of the more significant challenges in plastic surgery.
                Unfortunately, without pictures or a physical examination it’s virtually impossible to make specific recommendations in your case. In general terms, the nasal dorsum can be lengthened and augmented with cartilage and bone grafting techniques. The nasal tip can be remolded with a variety of techniques that are designed to reshape the lower lateral cartilages.

                If you’re considering correction of this type of problem, it’s important to consult a board certified plastic surgeon with experience in this area. This surgeon should be able to formulate a treatment plan that addresses your anatomic finding and achieves your aesthetic goals. 

An ethnic shaped nose such as you describe can be reshaped with rhinoplasty but the rhinoplasty surgeon MUST have vast experience and expertise in Asian rhinoplasty.  It is important that you consult with a board certified plastic surgeon or board certified facial plastic surgeon with extensive experience in this type of surgery.  Ask to see before and after photos of their own patients.  The rhinoplasty surgeon should also have substantial knowledge of nasal anatomy.  You want your first rhinoplasty to be your only rhinoplasty and these qualities in a rhinoplasty surgeon are essential.