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Thank you for your question.
I am Dr. Su S. and I will try my best to help you.
How old is he?
Which shoulder is affected?
Did he have any trauma, fall?
Which pain killer did you give?
Thank you for the input.Overuse of muscle can cause pain.Swelling is rather not common.It would appear soon after the climbing.There can be an inflammation or infection.Those can cause the swelling.At this stage, I would advise to get him an examination by doctor in person.He may need imaging like X ray or MRI scan.OTC anti-inflammatory pain medicine is not helping.You can apply warm moist compress.I hope this information will be helpful.
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Wish his healthy life.