Hehe, unlike most people on this site you're more correct about the time of onset- it's WAY more common when you are waking up than when you are falling asleep. But no- it's possible at either time, sounds like you had a dead-on SP experience.

I know it can be terribly frightening, especially with being unable to move. If you ever have it again, remember to remain calm and just remind yourself what it is and that it will be over in a few short moments. Wiggling your toes/fingers, your eyes, etc. should help- concentrate on the extremities which should be slightly easier to move to get out of it.

During SP you ought to be able to open your eyes and look around, so chances are if you can't or if you're seeing anything other than your normal empty bedroom, it's just a hallucination so remain calm

Also- lots of people experience euphoric and pleasant feelings and hallucinations during SP. Likely, fear is going to be playing a huge role in whether the experience is positive or negative. Try to read as much as you can on the topic so if it ever does happen again, you're nice and prepared and can stay calm, observatory, and appreciative of the cool experience it can be