Individuals can, but under normal circumstances most would speak to there doctor. If anything, the reporting by individuals would be up significantly now that vaccinations are such a controversial issue.
The fact that individuals/relatives can report potential side effects contributes to how unreliable the information is especially when taken out of context. Imagine having an indvidual like efed champing at the bit to report any unrelated ailment that a relative had in the day/weeks/months after a vaccination haha.
