This has happened when I pulled a hangnail on my thumb but I haven't heard of anything like this related to the vaccine.
Hope everything is okay.
Low platelets has happened in people after all 3 vaccines. There have been like 50 cases reported to VAERS after the Pfizer and Moderna shots and it is something to watch for in all the vaccines.
It's probably just a coincidence and he just pulled too much skin off, but it was an unnerving amount of bleeding.