What you described was not possession at all. Typically, this happens in the scene of the actual bedroom, when it's known as an out of body experience. The fact that you were still in dream mode simply tells me your brain doesn't switch out of dream mode well. You were feeling the same sensation, but since you were still dreaming you didn't have the "seeing myself laying in my bedroom" experience everyone else does. The choking is actually something called sleep paralysis. Don't worry, it's not as severe as it sounds. It's simply when your mind gets lucid to the fact that you're dreaming, but your body is stuck between dreaming and waking so it can't move. This is typically where people get the sensation that something "unseen" is holding them down. No, it's just your body refusing to let go of the dream and getting itself stuck.

Hope this helps!