Not all open bites require jaw surgery, however an open bite of 10mm is substantial. Having that knowledge alone is not sufficient to determine if jaw surgery is your only treatment option. All diagnostics records (X-rays, pictures, molds, etc.) are needed to determine is surgery is...
Since the entire lower jaw is longer on one side and shorter on the other, a lower jaw surgery would benefit you. It would not only align your chin, but would also correct the difference in length of the two sides
Looks like you are a two jaw casewith counterclockwise rotation and possible small genioplastyyou should get at least a 2D planningto predict some profile change
