Here is where they claim the increase happened, but they fail to mention how it fell just as sharply as it rose in the following weeks.

I see no evidence that their claim is for April, where you've drawn your red line. Also, this is a graph of hospitalizations, it is not a graph of how many are in the ICU and/or on ventilators.

Further, it only stands to reason that if they had been vaccinated, they would not have ended up in the hospital. She's not lying.