It’s difficult to give you an definite assessment of what’s happening without seeing you swing the club but I have a couple of ideas that should at least steer you in the right direction and then you can decide what you think.

Here goes…

1) The chest pain can be from overcompensating with your left arm (during the backswing) by ‘pushing’ the club back due to the lack of mobility in your right shoulder.

In other words, you’re trying to get some extra shoulder turn for more power into your backswing.

Keep in mind it might be due in part to a lack of trunk mobility in rotation as well. Meaning your upper body doesn’t turn well separately from your hips. When this is the case it may APPEAR to be a shoulder issue.

Or

2) You’re simply ‘muscling-up’ on the club using too much of your upper body in which case both improving shoulder mobility and hip strength should help relieve

I used to train a client who did #2 quite a bit and didn’t realize it but he had severe elbow pain for years. As soon as we identified the cause and put a program in place his elbow pain decreased significantly.

Hopefully this helps you out. Also, for shoulder and trunk mobility work on the exercises in the video, they should help.

I try to prevent shoulder pain when I practice my swing at the hitting range. I tend to have lack of flexibility in my right shoulder & on the follow-through of my swing, and then gradually a pain builds up on the upper-left side of my chest.
Is there any way that I can avoid this pain as well?

Thanks.