Don't run up stairs unless you are sure that your villain is afraid of stairs. Even then, it's best not to take the chance. Adrenaline makes people do crazy things. People have lifted entire cars before. I'm sure a stair-fearing psychopath could muster up the fortitude to chase a young, blonde, non-virgin up a few stairs if the situation called for it.
And by the way, don't scream like a maniac. It's okay to be scared. We'd all be scared. Just suck it up, gather your thoughts and play it cool. You don't need to act like Jack Bauer, but at least have a little self respect.