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Understand how to freeze a wart. Over-the-counter cold kits use dimethyl ether and propane to freeze the wart and the tissue around the wart. Realize that the wart will not instantly fall off after treatment. It may take several treatments and up to 3 or 4 weeks before the wart gradually disappears.
You may need to have a cortesone injection at the site of the injury, and then some physio to keep the shoulder mobile until it heals naturally. If the shoulder is allowed to 'freeze' then it could take a long tme to heal. I have had this condition and it has taken 10 months to overcome it using above treatment. This may not be the case for you but it sounds like what happened to me at the start, unfortunately I let it slide thinking it would heal by itself.