Assuming Heather McDonald collapsed due to COVID-19 vaccine

In February, the comedian Heather McDonald collapsed on stage just after making the following joke:

"I don’t mean to brag, I don’t care, but I want you to know: double vaxxed, booster, flu shot, and — I’m going to be honest — I have the shingles shot, too. And I still get my period — what? Yes! Traveled, went to Mexico twice, did shows, meet-and-greets, never got COVID. Clearly, Jesus loves me the most. Seriously. So nice, so nice!"

The collapse caused her to crack her head on the stage, and she was rushed to hospital (she is okay now). Naturally, anti-vaxxers took to the internet and immediately started claiming that the vaccine is what caused her to collapse - making  such statements as "sometimes it takes an adverse reaction to make someone finally wake up!".

Would it be fair to say that the Post Hoc fallacy is underlying these assumptions, or should they just be labelled as unsubstantiated claims?

P) Heather McDonald took the COVID-19 vaccine

P) She later collapsed while performing

C) The vaccine made her collapse

Yep, this is the post hoc fallacy - because her collapse came after the vaccine, the vaccine is asserted to have caused her collapse (which doesn't make sense - I tend to wake up after the sun rises, but that doesn't mean sunrise is what wakes me up).

It's also confirmation bias on the part of anti-vaxxers. There are plenty of people (myself included) who took both vaccinations and did not collapse as a result, yet we are routinely ignored when anti-vaxxers try to peddle claims like the above. Even if the shot does cause adverse reactions for some people, this isn't representative of everyone who got jabbed, and it's dishonest to claim otherwise. Yet, anti-vaxxers will pick on the minority who suffer from side effects and say "SEE! THE VACCINE IS FAKE!" or some related nonsense.

Hi, KDU!

Would it be fair to say that the Post Hoc fallacy is underlying these assumptions

It would be unfair, so far. Logical fallacies are mistakes in arguments. In order to fairly accuse a person of committing a fallacy, first you need to identify their argument. 

or should they just be labelled as unsubstantiated claims?

The only other option you lay out for any of millions of strangers who might visit your question, with all sorts of differing views and opinions, is that the anti-vaxxer’s claims are unsubstantiated. This is a loaded question fallacy. There appears to be controversy over whether the vaccine is safe. No matter how much you may regard an anti-vaxxer as mistaken, you must be careful to not yourself commit a fallacy while critiquing them. I don’t know whether the claims are substantiated. 

Thank you, KDU.

From, Kaiden

I can see where one might be tempted to dismiss this as a fallacy, and certainly with cause, but on its face, it seems more of a confirmation bias on the part of anti-vaxxers. 

There's a fascinating podcast on NBC right now about a nurse Tiffany Dever ( I believe) who had the unfortunate experience of fainting on TV as she received the Covid Vaccine and launched a hysterical response all over the world from conspiracy theorists who claimed she had died or disappeared afterward.

So, medically it's not unreasonable that one might faint as a result of the vaccine. In Tiffany's case it was a physical reaction to pain that she was susceptible to. There are too many variables to assign to the effect of the vaccine. We do know statistically that such a reaction to the vaccine is reasonably low, while fainting as a result of being infected by Covid -19 is more common.  Was it established that she did not have Covid? We have found that infection is still very high even among those who have the vaccine.