Since you can’t post links, do a Google search for:
“paul offit wired” and read the Wired article. Paul Offit developed a vaccine and is an expert in the field. He stated (and this was used against him as a sound bite) that the body can handle 10,000 vaccines at once.
In 99.99% of cases, vaccines will do no harm.
BTW, the Tifferes Yisrael called Jenner one of the Chassidei Umos Ha’olam for his smallpox inoculation. People who don’t vaccinate are not only ruining it for their kids, but they are ruining it for other children as well due to the herd.