I think it sounds like the "catch-up" drill too. As others have mentioned, you may not be rolling enough.
Someone else asked about when during the stroke are you feeling the pain, this is important information for figuring out why it hurts.
During mid recovery = probably a roll issue
During hand placement in the water = likely your stroke is too narrow or you're even crossing over
During the initial part of the pull phase, the "catch" = probably poor arm position and/or weakness in the stability muscles
This is a really good drill in general for improving form and body balance in the water, so it's worth trying to figure out why it's not working for you and how to fix it. I'd strongly encourage you to ask the coach about it. Tell him it hurts your shoulder and you want to make sure you're doing it right. Then have him watch your form.
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