is there a non surgical way to fix my facial asymmetry? (Photos)

Yes, Botox in combination with radiofrequency treatments and/or fillers, Sculptra can be used to improve symmetry of the jawline. See an expert. 

Thank you for sharing your question and photographs. I can see your area of concern and the treatment would depend on which side you favor.  You can treat the overactive teeth grinding side to reduce the bulk of the masseter and temporalis muscle, hopefully breaking the reflex to grind, or you can add dermal filler to the right side to better match the left. Either way you should be able to improve upon the asymmetry.  Hope this helps.

While Botox could be injected into the more prominent side on which you say you grind your teeth, it would take years for the muscle to atrophy enough to notice any significant decrease in the bulk of that side of your face.  Adding filler to the other side would be a much more immediate and gratifying option for the smaller side of your face, but you would need someone who has extensive experience in filler to be injecting into those areas.  Additionally, although the Botox may not make a significant effect on the bulk of the muscle, it could help reduce any other symptoms or problems you may be experiencing from the actual grinding of the teeth.  Best of luck!