How should I approach getting a prom date?

Warning: This is not a short read. My failures are extensive.

Let me give you some background: I'm a high school senior, and I've never had a girlfriend. I do have a social circle, and lots of guy friends I talk to regularly, but I just don't talk to girls.

My high school prom is around the corner--only a month away. I've asked a handful of girls in my social circle, but they all said they have dates already. (not sure if I quite believe that)

I've gotten so desperate that I also asked a few girls that I've had classes with in the past. Since they weren't even part of my social circle, I don't even have their numbers or emails. So as cringe worthy as this is, I asked them over facebook.

One girl straight up asked "is this a joke?" because I didn't ask in person. And when I said I was serious, she said that she had other guys ask her already and that she wasn't sure yet and that she'd keep me in mind. Assuming this to be a "no but too nice to say no" answer, I just said okay I'd look elsewhere.

I don't know girls. I'm not friends with girls. So I know it's a bad idea to do the showy, make a scene promposal.

And I have no idea what to do.