That said, I think the medical safety of vaccines is far from clear.
There is overwhelming evidence that vaccines improve public health. Given that science can only ever disprove a theory, the "far from clear" phrasing tends to be convenient if you don't want to believe something. It's a phrase that can be applied to just about any scientific theory, regardless of how successful it is.
Last year, a friend of mine's kid got a series of vaccines, and that night went into seizures and nearly died. The hospital treated it as a mysterious brain problem unrelated to the vaccines.
Maybe it was a brain problem unrelated to the vaccines.
(While I have a newborn myself and can imagine the stress such a situation would cause, your story is an example of availability bias.)