It could happen (i don't know if that's what happened in this case), but it would be an outlier. For instance, there are some deaths tied to the vaccine as well. What a vaccine does is force an immune reaction. Typically this is mild and merely trains the body how to react for when it's attacked for real. But in some instances there would be severe swelling, which could cause damage and scarring depending on where it is. And in really severe cases could lead to anaphylaxis and death.
But whether or not her original tweet was accurate is not even the point here. She dared to deviate from the approved political directive. When chastised for such instead of apologizing and retracting her statement (as is far too common when this occurs) she did the unthinkable. She called out the fact that there ARE political directives that blacks are expected to follow, even to there own detriment.