Is it possible to make the alar rim thinner? (photos)

Thinning the alar rims is possible but rarely indicated, however in your case you would benefit from it, you must accept a thin scar just right at the edge of the alar rim; it is a precision work of high risk, is slicing out a thin portion of the central rim preserving the outer and inner linings without making a retraction or a necrosis.Agree your nose works are or very poor quality; I recommend full rebuild of the tip to lower it, reshape, redefine and obtain an harmonious result without the pinching effect.Your case is a great challenge, what an interesting case for the right surgeon.Beware who you choose, it is a top difficulty case.

Thick skin will be an significant impediment to seeing any further refinement in the tip of the nose. The thickness of the skin can sometimes be contributing more to the bulbous tip than  the actual lower lateral cartilages of the tip. The sidewalls of the nostrils are very difficult to thin out, since there is no cartilage in that area and it is fibrofatty tissue. It's important not allow any collapse of the alar rims. Look for a very experienced rhinoplasty surgeon for any further refinement

Firstly your columella, is hanging low, the tip is too ball-like and your skin is thick.There is an operation to take a wedge out of the alae but few surgeons do it because of visible scarring and possible distortion.Your tip need refinement. What exact surgical procedures cannot be determined just by  seeing a few pictures. You need a good surgeon.