The first amendment absolutely gives you the right to lie, and the right to profit from that lying if you're not explicitly committing fraud or defaming anyone. You may disagree with it, but that's what the law is.
You don't have a right to lie.
This is defamation, which is also against the law. However, the damages here are incredibly minor, and thus not worth punishing. Most people probably don't believe you.
However, if I made a lie about you that caused you to lose your employment and become unhireable, is that also protected speech?
You don't have a right to harm others with lies. You don't have a right to lie.
I'm aware. That's why I mentioned it. There's no remediation if there's no damages.
If I'm made of marshmallows I'm not human and not eligible for health insurance. If my insurer believes your claim which is a reckless disregard for the truth and I'm denied coverage, you're liable. If my wife leaves me because she didn't want to marry a marshmallow and causes massive legal damages and emotional harms you're liable for defamation.
It's like you're arguing you have the right to punch. Like, sure, swing your arms wherever. But your right to swing your arms ends at the tip of my nose.
You don't have a right to lie about me.
However, there are very specific exceptions. You are not allowed to lie under oath. You are not allowed to defraud. You are not allowed to defame. Those states are each defined separate and apart from “lying,” which is freely permissible.
Also, doctors and lawyers are subjected to discipline by their respective guild. So even if it's your right to say bullshit, you might lose your job and license.
Arguably, there's no to little consequence of being a nobody and lying about something like autism and vaccine. It's probably isn't worth the effort to sue folks. That said, misinformation is clearly harmful and we shouldn't let people lie unchecked.