Hi, I too experienced something similar to what you describe, and from researching about it I believe there is nothing to worry about. It has been linked to the sleep disorder, Narcolepsy however, but only when it's at the onset of sleeping not when you're waking up. When we sleep we we are usually paralysed anyway to prevent us from acting out our dreams in REM sleep. You are waking up before the hormone that numbs our muscles has has worn off.
They just term it sleep paralysis, although it was termed the 'Old Hag syndrome' initially, as some people experienced hallucinations during this period and attributed it to paranormal phenomenom before science could explain it. With regards to being able to respond to an emergency - as you're just becoming conscious before your body's ready, your response to an emergency is the same as if you were actually sleeping.

If it is starting to interfere with your sleep though, it's worth just checking it out with the doctor.