I guess both. I can‘t tell quite well what exactly happened but she definitely beat Kokoro with some item (possibly chair). To the head because we see that Kokoro lies on the table, saving Naoi.
Kurumi could faint simply out of shock of what she just had to deal with
There's no indication that Kurumi hit Kokoro over the head. She fainted due to illness and her fever. Her hand was only showing her losing her grip on Kokoro's shirt, which you can see due to the screentones used for it. Plus, the sfx used for it "ずる" means to slip off. Kokoro is leaning over Naoi's body because she's still strangling her.
If anyone struck Kokoro with an object it would've been Kudou, because Kurumi was looking at her one moment, then the next moment the chair Kurumi's looking toward is empty. But it's hard to say exactly what happened. This could end up being another one of Kurumi's disassociation episodes.