That is just being a good parent, you should never take big daddy's word for anything.
Why are you more qualified to do that than your doctor?
First, my child is MY responsibility for their safety and well being.
You didn't answer, why are you more qualified than the doctor to know what is safe and what isn't?
Do you think the medical industry is any better than any other industry? Unfortunately the majority are idiots just like every other industry, and the minority that are not carry the weight of the system and competence on their shoulders.
Industries don't do bad stuff because they're idiots, they do it because it helps them make profit. Fortunately, there are all sorts of trials that have to be done before a vaccine is approved and all sorts of regulations, so vaccines are not in any way dangerous now. If you're still not fully trusting, ask a doctor, or two, or three, or whatever. You don't have a medical background and you won't really understand what the stuff you find on the Internet is, or if it's trustworthy.
Also, an intelligent person in my field, in programing, robotics, bio engineering and hundreds of other fields would be great doctors...it's just they learn different skills instead.
Oooh I get it, you think you're gonna get better than the doctors at their job. Don't do that, it's dumb.