An asymmetrical jaw is due to the individual skeletal/bone development, and it is usually a result of the bone being off to one side that then causes the bite to be less balanced. In general, many of us are asymmetrical, and many of us favour chewing on one side more than the other. However, the severity of the asymmetry may result in the jaw being longer on one side than the other side, creating a slant of the biting plane of the teeth, which may cause you to bite more on one side than the other. This is probably the reason why you have muscular hypertrophy on one side more than the other (muscles are bigger).
Unfortunately chewing on the other side during eating may not help the situation, and if you add pressure to one side of the teeth and not the other, in the long run, it may cause other issues as well as you are overloading one side preferentially. Nighttime grinding (i.e. bruxism) is also another issue that we cannot avoid as it is done subconsciously.
To correct your jaw asymmetry, the severity of the asymmetry could be assessed clinically by an orthodontist and/or an oral maxillofacial surgeon. They will be able to advise you on the treatment options, such as jaw surgery to correct the bony imbalance and centre the chin, or perhaps a more conservative option such as selective botox injections, to reduce the more prominent muscle. They will also be able to assess your bite to see if orthodontic treatment is able to even out your bite better.
Reference:
1. Martinez-gomis J, Lujan-climent M, Palau S, Bizar J, Salsench J, Peraire M. Relationship between chewing side preference and handedness and lateral asymmetry of peripheral factors. Arch Oral Biol. 2009;54(2):101-7.
