My face is short and wide. Will Jaw/chin surgery give me a longer/bigger lower face?

A bimaxillary advancement orthognathic surgery with clockwise rotation would tipically augment your lower facial height, improve your chin and mandible projection, and better define your jaw border. 

Your issue could be resolve with a jaw surgery. You would have to see a knowledgable orthodontist And OMFS to plan the treatment. 

you are correct in noting that the lower face height must be in balance with the rest of the face. It does appear that although you noted  the 'bite' is fine, you may have the lower front teeth 'tilted forward' to make the 'over bite' seem less/absent. Since the lower front teeth push forward the lower lip, the 'fold' under the lip gets deeper and emphasizes the lack of height. As to increasing the height, it is definitely possible either via a sliding genioplasty approach or more involved treatment if the xrays would show some features of a short face development pattern