Your thick skin hides any minor asymmetries that could occur from surgery, but it does make changes more difficult to see, and I think you recognize that by your question.
See a surgeon comfortable with such situations, but improvement is certainly achievable.
Making the nose smaller is one of the most common changes made during a cosmetic rhinoplasty. Reduction rhinoplasty can come at a cost of sacrificing some degree of nasal breathing, so go to a surgeon who discusses this with you as well as ways to preserve as much airflow as possible.
Overall you have a nice result with one exception. You have what is called a hanging columella which makes the nostrils show too much. A very common problem that is easy to fix. In less than an hour with closed rhinoplasty. This is something I often see with open rhinoplasty if you had it done...
