Ben (from your YouTube account name),
When I watched your video in slow motion, your pitching arm appeared to be "dragging".
Since you mentioned that your elbow hurt after pitching, it signaled stress on the elbow.
I observed your elbow bend too quickly for you to produce your "whip" motion like a catapult launching. Ideally, you should form your "L" shape with the Ball points away from you, which will be the farthest point for the ball to be away from you. Your elbow went ahead of your shoulder turn. It means you are pitching more with your arms/elbow instead of generating the torque from the body turn.
My advice is to work with a good pitching coach to break down your mechanics first. Record yourself and watch in slow motion.
Good luck and enjoy baseball always!