Translate your last paragraph.
In other words, there is nothing in the story you’ve given to show that the vaccine caused this. Maybe it did, but there’s no evidence of that here. Post hoc ergo propter hoc is the logically fallacy that something happening after something else must have been caused by that something else. It isn’t necessarily true. In fact, it hardly ever is.
If I give a glass of water to 1,000 90 year old men and then monitor them all closely for the next month, some of them will die. Did the glass of water kill them? Should we declare that water is a deadly toxin? Or do older people sometimes die from a variety of causes?
Again, I do sincerely hope your co-worker’s son recovers and I hope they figure out what caused the medical problems he’s had. But there’s nothing presented here to suggest the vaccine is the cause. Yes it’s possible it somehow is related, and if it is, I hope that’s found out. But it’s just as likely - if not moreso - that it’s unrelated.