Looking up stories of it at 4:00 AM and trying to understand it after waking up from it is not a good idea.
I've experienced it a number of times before. It's not "demonic", though it is creepy. It's caused by being in a between-sleep-and-wake state, thus it's like dreaming while awake, so it can include auditory and visual hallucinations, which are often disturbing.
Paralysis naturally occurs during REM sleep (if it doesn't occur, then you sleepwalk, which is a different issue), and ideally you wake up at the same time the paralysis ends. But sometimes you become conscious before the paralysis (and the dream) ends, hence sleep paralysis. Paralysis naturally causes a heaviness feeling in the chest, which is why in the middle ages, people thought it was the result of a demon sitting on your chest (and the association of sleep paralysis with nightmares didn't help either).
One time during an episode of sleep paralysis, nothing actually creepy happened at all, though it was still hallucinatory. I just experienced my roommate walking over to me and speaking to me while I was lying in bed. When I woke up fully I saw that he was still asleep, so that had just been a hallucination. It was bizarre, but it didn't feel creepy to me.