How Can I Correct my Asymmetrical Nostrils?

Rhinoplasty with attention directed to the tip and nostrils is performed to make the nostrils more symmetrical. In addition, any warpage of the dorsal cartilaginous septum can be shaved down to give it a straightening effect. Any columellar show is also trimmed both membranous and columellar septum when the end of the caudal septum is warped creating asymmetrical nostrils. This is all done through closed rhinoplasty techniques as outpatient surgery.  

There is no such thing as surgery without scars at least not until we reach the start trek or star wars period of time. Anywhere you get an incision you will get a scar. The plastic surgeon is trained to weight the trade offs of final scar and surgical approach to give a specific result.

Your photo only gives a single angle of view so your question cannot be answered specifically. In general though I see the tip asymmetry you describe and think this is a combination of septal deviation and asymmetric nasal dome cartilages. The surgery required would be septoplasty to straighten the septum and open rhinoplasty to adjust tip cartilage positioning with sutures. In my experience open rhinoplasty is the most reliable approach.