There are a variety of rhinoplasty techniques for fixing an upturned (over-rotated) nose. The basic principle is to bring the tip of the nose down, restoring a more normal angle between the upper lip and the nose. This angle should be 90-95 degrees in men and 95-105 degrees in women, ideally.
The tip can be counter-rotated by shortening the medial crura of the tip (lower lateral) cartilages, which sit behind the columella, the portion of the nose between the nostrils. This maneuver, called a medial crural overlay, will also reduce the projection of the nose, the degree to which it sticks out horizontally. from the face.
Another commonly used technique in rhinoplasty is to place extended spreader grafts, long straight pieces of cartilage which are sutured to the septum and push the tip downwards. These grafts may be taken from the septum or from rib cartilage, if the septal cartilage has been previously utilized.
Visibility of the nostrils should improve with the techniques I mentioned above. Additional maneuvers, such as the placement of rim grafts, can also lower the nostril rims.
There are no effective non-surgical ways to counter-rotate the nose and reduce the visibility of the nostrils. If your issue were simply building up your bridge to make your nose appear less scooped, this may be achieved with the use of filler, however, I would caution you to avoid any permanent fillers in this area.
Best of luck,
Dr. Mehta