I don't think that sounds like a demon, but if it is I'd start looking into charms, or a religious symbol necklace, like a pentacle, or certain crystals.
From what you desribed it sounds like a possible shadow creature. I might be wrong, but that first feeling is associated with them. Could also be a poltergeist, or angry ghost.
Mabey an astral traveler, not sure how that would work...