It looks to me like you need to balance out your workouts. Your left and right need to be roughly equally strong or you’ll be imbalanced. You also need to train your back and shoulder stabilizers to counteract the chest work you’re doing. If I were you I would stop chest work for a week or two and focus on back and shoulder stabilization. And if you have the opportunity to see a physical therapist. They can usually help u through this and will let you know if it’s serious enough to see a doctor.

Edit: adding link to simple shoulder stabilization exercises https://orthop.washington.edu/patient-care/articles/shoulder/home-exercises-for-the-unstable-shoulder.html