I can’t really tell if it was a dream or not, but last night I woke up into sleep paralysis and couldn’t move my arms or body, I was just wondering if waking up into it and not being able to move your arms is actually possible? I didn’t open my eyes because from what I’ve read if you wake into sleep paralysis it’s the most likely time you’ll see the Old Hag 
Sleep paralysis is a hard nut. You could say you’re awake, because you are conscious, but I think you’re awake at the moment when you can move again. Possibly when you see your room it’s just an illusion, which can lead to OOBEs or LDs.
Sleep paralysis occurs when we are awake, inside our physical body which is still asleep.
It is possible for the physical body to be asleep and the mind to be awake (or concsious). So when this occurs, we wake up inside our head, with our mind, and when we try move we obviously can’t because the physical body is still asleep.
So, yes, waking up (with your mind/thoughts) is possible, while your physical is still asleep, and in a paralysis state. Happens to me often.
Yes what the others said… And about the old hag , I dont think you actually see an old hag , its just the name of the phenomenon in which you feel a pressure on your chest , you dont actually see an old hag.
There have been times that people have seen what they refer to as an “old hag”, I dont know too much about that however had an experience once where I woke up in SP and looked to my side, and saw some guy with a shotgun pointed right to my head. I guess you can call that the old hag syndrome, however its only “fear” based, if you are not afraid you can just laugh at him/her.
Nooooo, I think Old Hag is referring to a hallucination of something on your chest which the mind uses as an explanation as to why you feel pressure on your chest.