This happens to me every so often. Sometimes another being is present, sometimes I'm alone. Sometimes I wake up out of the dream, feeling sheer anxiety. Sometimes I stay in the dream, and it passes or I end up wrestling with some monster from under the floorboards.
The moving from room to room suggests there is a lack of agency. I personally see the bed as an intimate place, with oneself and with others.
Do you do any breathing exercises before you go to sleep, or any other calming activities before bed? I've found that lavender tea and lavender essential oil are really helpful with this stuff.
Also, it might sound woo woo, but I encourage acting like there is an external force doing this to you, and to get angry at it for affecting you this way. Even if its simply reinforcing to yourself that you don't want to be stuck in a loop of paralysis, it might help jump you out of a rut. Sometimes when I am having a bad dream I pretend that someone else is playing a bad prank on me, and I start (internally) yelling at that person. It typically makes the anxiety dreams subside, whether because there is truly another person/entity or because feeling angry reassigns me to feeling power (rather than fear or anxiety) in tandem with my anger.
I hope this helps.