For example, what is the longest recorded delay between a vaccine being administered and a side-effect being observed? Vaccines trigger an immune response but aren't in your body for a long period of time, so you typically see reactions within a few hours or days — the record is something like 6 weeks, so multiple years would be quite the outlier.
https://www.cdc.gov/vaccinesafety/concerns/concerns-history....
The other key thing to remember is that this isn't some hypothetical question about risks in absolute: your odds of being one of the very few people who have a significant vaccine side-effect has to be weighed against the much higher probability of having significant health impacts from COVID-19. “Neither” is not an option any of us get to pick.