To start, I'm not a coach so I don't wish to discredit your coach, I am only offering my advice as I see it. If any of my tips contradict anything a coach has told you, ignore me. I can only speak about what works for me.
Your footwork seems relaxed and fluid, which is very good. Looks like you aim your shot well and cover your mark. You may not necessarily need a better pair of shoes. Your flaw there may be in how you are making that last step. You shouldn't be planting the left; rather, you should be planting the right and pushing off your right foot as you slide on the ball of your left, toward the foul line.
Give it a try by practicing without a ball. Take the last three steps of your approach. Walk it slowly, step off the left, plant the right foot and slide to the foul line. If you can slide on the ball of your foot, your shoe is fine. If it doesn't slide easily, try some "EZ Slide" from the Pro Shop - a pouch of that with one tap (trust me, you don't need much) on your slide foot will work wonders and save you big money over buying a new pair of shoes.
When it comes to your elbow, imagine your arm from shoulder to wrist as the string on a yo-yo and the ball as that yo-yo. Swing the pendulum. The more fluid that motion is, the less strain on your shoulder and elbow and you won't feel like you're pushing the ball across the foul line. It should just roll out of our hand on the follow-through, thumb first and fingertips last. From what I can see your release is good and when you landed your mark, the ball moved well for you into the pocket, often for a strike.
Overall, you look comfortable and confident out there and that, more than anything will help you focus your game. You're well on your way.
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