Relieve pain, prevent injury, and increase performance. Get customized mobility coaching developed by Dr. Kelly Starrett.
How is your shoulder range of motion? If your left shoulder has less range, that could be causing you to pull the bar forward on that side? Is the asymmetry just at the shoulder level or can you see it in other parts of your body as well? Is anything else angled or slightly off kilter? I find it helpful to video from front/back and the side while doing an exercise to better analyze form.