Indentation on the left side of my nose, how can I fix it? (photo)

The alar cartilages form the tip and the alae, the lateral crura (side leg) of these cartilages shape the side of the tip and ala and provide support as well as functional allowance in breathing; this essential part of the aesthetic and functional nasal skeleton is always, by the anatomical canon, more or less convex (belly outwards). If it is too convex may be unsighty and prominent, a moderate or slight convexity is considered beautiful; if it is flat or with a slight concavity is still within normality margins and leads to a nice nose too, without functional impairement.
However, some individuals may be born with a congenital abnormality by which part or the whole of the lateral crura of one of both sides can be moderately to severely inverted, concave, hollowed inward, with the belly facing down side and the dip to the surface. This is a guarantee of self-consciousness and dissatisfaction by patients suffering such aesthetic irregularity and, in many cases, also a functional impairement of higher or lesser grade.
The inversion can be partial affection only a portion of the lateral crura or total (the whole crura inverted, literally like a pistachio shell), and the issue can affect one side or be bilateral (both lateral cruras inverted, in partial or total grade); when bilateral the inversion can be symmetrical or asymmetrical in grade, location and shape; all the former leads to a multiple number of combinations and varied clinical presentations.
This odd deformity is considered "irreparaible" by many surgeons, as weird as it sounds, I talk by own experience by the tales of patients reaching my office bounced from many consultants before my advise. In the medical literature there are series of few cases published, in my experience of high-end rhinoplasties I have done nearly 100 of such cases and have my own protocol to manage this deformity, which I try to summarize briefly now:
IDEAL CASE
-Bilateral, complete or subtotal and symmetrical inversion of moderate grade of concavity: this is considered the ideal case, although can be highly deforming to the nose (a beak shape, or clipped); the solution is the cross-located eversion of the lateral cruras; by means of open approach rhinoplasty the cruras are freed from the lateral attachment to the accesory cartilages and severed near the domes at the point of the inversion starts, then they are very carefully (not to damage them) freed from the underlying mucosa and everted by flipping them upside down, however... this maneuver makes the caudal (lower) edge of the cruras become cephalic (upper) and viceversa, making necessary cross-locating them (left on right side and viceversa) to achieve a perfect anatomical match, and suture them back in the new place. Some surgeons have proposed treating this condition without this delicate dissection and meticulous maneuvers, vowing to tutorize the cruras with batten grafts, simple suture plication, etc; I am totally against these "simple" and "easy" procedures, the failure rate is very high and the results not very harmonious commonly.
NON-IDEAL CASES
Here the surgeon must deploy all his resources, skills and creativity, so there is not a clear solid protocol; I will list some (but not all) common non-ideal scenarios of lateral cruras inversion, requiring other technical solutions:
-The same ideal case but with a high or deep grade of concavity: when you perform the technique describeb above on a nose with very hoollow cruras happens to build exactly the opposite problem, a boxy or square nose with overprominent (too convex) cruras. 
-Incomplete inversions: only a portion of the cruras is inverted, then not a complete cross-located eversion has to be done, but only a sectorial eversion and cross location.
-Assymetrical inversions: you can't cross-locate portions of crura everted but of different length, width or shape.
-Irregular inversions: some cruras are like a streamer or a carrousel, with odd and atypical random configurations, becoming thus irreparaible.
-Unilateral inversions: you can't cross locate the affected crura in exchange of a non-flipped contralateral crura and, therefore, you can't flip the inverted crura (or portion of crura) to evert it.
Regarding the non-ideal cases the list of techniques, alone or in combination among them, adequate to successfully address the case are varied:
-cartilage plasties: may modify slightly the curvature and grade of inversion in order to match the contralateral side
-batten grafts: only only in extremely weak cruras (e.g. filipino noses or other of arab origin)
-sectorial replacement graft: when a portion of the crura is deemed irreparaible and has to be removed and bridged by a fresh and well-shaped portion of cartilage
-total crura replacement, uni or bilateral: when one or both cruras are deemed irrepairable, or when the eversion leads to a over-convex / prominent nose, or in random grotesque deformities (streamer cruras) or when the assymetry in shape and size lopsides the tip... the best solution is not fighting impossible battles and be terminating: brand new cruras, hand made out of ear cartilage grafting.
Finally, the rest of the nose and tip can be treated in an ordinary manner, once the crural inversion has been addressed.
The final choice of the adequate technique for these inverted cruras is made always always intraop based on findings and tissue behaviour.
With all that said, seems you have an unilateral partial deep grade inversion affecting to only the central third of the left lateral crura (note: you do not have any kind of affection or inversion of the upper lateral cartilage, you suffer inversion of the lower lateral cartilage, aka alar cartilage, at its lateral crura); in these cases the most common and successful solution happens to be removing the inverted sector and replacing by a portion of cartilage. 
You need the advise of a very very good surgeon with solid experience in inverted cruras treatment; do require, demand, condition him to show you intraoperative images of his cases, as proof of mastery. Do NOT accept under any circumstances fillers or other magic solutions. In good hands correction is guranteed.

Judging from the single photograph, I do believe the depression can be corrected with an open rhinoplasty with cartilage grafting.  Good luck and be safe.Respectfully, John T. Nguyen, MD, FACS, FICSDouble Board Certified Plastic SurgeonAmerican Board of Plastic SurgeryAmerican Board of Surgery

A rhinoplasty procedure can accomplish fixing the indentation on the left side of the nose. A spreader graft can be placed underneath the concave upper lateral cartilage, and in onlay graft can be placed over the lower lateral cartilage to make the nose more symmetrical.  Digital computer imaging would be helpful in communication process to understand what can be accomplished. For more information and many  before-and-after  Closed rhinoplasty examples, please see the link and the video below