Can I get jaw surgery just for side profile appearance? Mouth sticks too far out of my face.

It maybe that it's only your teeth are out. This might be corrected by braces alone. An X-ray helps. 

The 'natural' look of faces from many cultures/backgrounds does vary. Depending upon the 'tilt' /fullness' of the teeth, orthodontics with or without jaw surgery can alter the look. Also, genioplasties can 'offset' the fullness of the lips in some cases. A maxillofacial surgeon should be consulted