Last night I experienced sleep paralysis for the first time

I honestly don't know if this was a dream or sleep paralysis but the experience was so similar to how people describe sleep paralysis.

First, I think i knew what set it off. I'm staying at a friend's house so its not an environment I'm used to. When I was falling asleep, I closed my eyes and was looking around the room, I could see the general shape of the room through my eyelids, like it was overlayed with vague image of the room.

When I started experiencing sleep paralysis I recognized it instantly. I knew if I opened my eyes I would likely see something in the room so I kept my eyes shut out and was overcome with fear.

Next thing I know I feel a presence approach the bed and the whole mattress began shaking. I tried screaming and nothing came out, like my jaw was wired shut.

Then the shaking stopped, my eyes opened for a moment, and screamed. That part must've been a dream because no one responded, or acknowledged anything about hearing a scream last night.

Either way it was terrifying and I don't know if it was a dream or sleep paralysis. Can you even expirerience sensation like shaking or touch in sleep paralysis?