This is all misinformation.
The vaccine significantly reduced severity of infection, likelihood to become infected at all, and likelihood of transmitting there infection.
The side effects impacting periods were incredibly rare, mild and fully disclosed.
Children's test scores are still substantially lower now than pre-covid, likely some of that is due to brain damage from the covid virus (remember that the "brain fog" was a common symptom for weeks or months, sometimes longer) and many children died or developed serious health issues like diabetes from the virus.
But needles are scary, so some people will claim anything to justify their aversion rather than admit they have a phobia of injections.