Just guessing here, but has he been evaluated for possibly adhesive capsulitis (frozen shoulder)? Maybe the flu shot was some sort of triggering event? I am not a doctor.
Yeah, on the occasions when I gotten flu shots my arm would be just a little sore for a day or two. The last time I got a tetanus update it was very sore for over a week.
See if his doc reported it through VAERS. Complications are rare but they happen and can be severe or even life threatening. In the unlikely event that it results in a permanent disability or condition, there is a government compensation program for it.
This year I got a flu shot for the first time in 4 or 5 years. It didn't hurt the day of, but it felt like they shot concrete in there the next day, and for a week after! I ever had a slight lump at the ejection sight.