I'm in Canada and we do have an official way primary care doctors and public health officials and report and have adverse conditions investigated. The problem is that when a patient presents with symptoms that started shortly after the vaccine administration they are often dismissed by their primary physician. Often the doctors even do scans or blood work and they find "nothing" and deem the person being okay. Rather then doing further investigation the patient is often treated like they are making up symptoms or exaggerating. Basically they treat them like an anti-vaxxer instead of properly investigating their condition. They just tell them not to worry "it'll go away".
We have people who come in to get additional doses and they'll mention having some pretty serious symptoms after their last vaccine and we will be so surprised with how often we are told they went to both the hospital and their family doctor and got zero resolution and the doctor did not report it to public health.
In many cases we just seem them medically inelligble in these cases and tell them they need to go to their doctor and followup more to ensure they will be safe to get another dose.
And this is where I think a lot of the problems with vaccine mandates and pressure from employers can lie. You end up with people who feel like they have no choice to get the vaccine, they have a bad reaction to it, and then doctors treat them like they are lying or that it's no big deal. Then they go for their next dose feeling even more untrusting of science and get another vaccine.
We are ruining a lot of people's trust in science and medicine by how hard these things are pushed. Because of how much push back there is against anything negative with vaccines, it means doctors also often end up with this same bias. They are afraid to attribute any problem a patient has to the vaccine.
I have no problem with vaccines and have 3 doses currently. But I can empathize with these people who feel hesitant and I myself definitely have lost some faith over the last year of doing this work.
It really seems like a lot of scientific and medical standards have been tossed out the window because of politics.