To feel paralyzed in a dream is very common. When you are not sleeping deeply, your mind becomes aware of the fact that you are not moving in your bed and the illusion of your dream is broken. Your mind assumes you are paralyzed in the dream world as a way of explaining the sensation that you are not moving in your bed.
Symbolically, to be paralyzed in a dream may represent your feelings of lack of control. You may also feel an inability to prevent something in which you want to stop.