It's true that systematic surveillance of vaccine side effects is poor. For example, even when HPV vaccination of teenage girls became a thing, one of the obvious side effects you'd guess will freak out teenage girls (changes in menstruation) wasn't tracked very well. We genuinely don't know beyond "Clearly not drastic enough that it caused significant medical problems" whether this is something that was noticeable above background levels.
However one problem we have is that for mere side effects ("My arm aches a bit", "My period was a week late", "I feel kinda sleepy in the morning") we don't have good baseline data to compare with. I'd quite like to see someone study, e.g. if we change the Facebook blue colour slightly, and ask a study cohort, what medical "side effects" do they report for that? Clearly someone in a large survey population will report that their right thumb hurts now, and we can reason (but not prove) that's not going to be a direct result of the CSS change, but measuring what this noise looks like would provide a baseline for low risk vaccinations.
One other reason more studies would be useful, is that for the person I know, this happened after the first dose.
That means that at the moment there's just no reasonable way to decide whether it's safe to get a second dose or not. If there were studies that would show that almost nobody has a lasting head pain post vaccination, then one could conclude it's probably just a super weird coincidence, and take a risk with a second dose, to at least get the full protection against covid-19.
Without data the most prudent thing is to do no further harm to oneself, and live with increased risk of infection and all the restrictions and increased costs that are put on unvaccinated.
[Posted in case it provides a data point for your friend to discuss with a local doctor, not to debate this doctor's affiliation, credentials or motivation. Would love to see more presentations of physical evidence from autopsies and lab tests, to complement statistical studies.]
Though at least with pain, you could compare with previous reports from that same person. Pain started day 1, never subsided until 2 months after. Pain starting at 2 months is probably not a side effect, unless it's something that consistently shows up in the data after the same period of time since vaccination (background noise would not).
Maybe add a self-reported intensity scale for the symptoms.
Anyway, I can see why studies like these can be hard.
However one problem we have is that for mere side effects ("My arm aches a bit", "My period was a week late", "I feel kinda sleepy in the morning") we don't have good baseline data to compare with. I'd quite like to see someone study, e.g. if we change the Facebook blue colour slightly, and ask a study cohort, what medical "side effects" do they report for that? Clearly someone in a large survey population will report that their right thumb hurts now, and we can reason (but not prove) that's not going to be a direct result of the CSS change, but measuring what this noise looks like would provide a baseline for low risk vaccinations.