Whoever said "They calm down once they're neutered" lied!

My cat is driving me crazy. She wakes me up at 5am by literally knocking on my bedroom door. She attacks my legs and feet, leaving me scratched and bitten. She spills her water dish on purpose, every day, because she likes to play in it. She drinks out of the kitchen sink whenever the water's running. She plays in the shower--while I'm in it--and knocks everything down. She runs from one end of my apartment to the other, at least five or six times in a row, on my hardwood floors in the middle of the night. Whatever she can knock down, gets knocked down. The list goes on, and on, and on.
A few months ago, I thought about giving her away. And I cried. She's been my kitty since birth and I love her to death, but she's driving me crazy!
I took her to get neutered a short time ago with the hopes that she would calm down and sleep all day like most other house cats I know. Wrong. Whoever started that myth is a trouble maker because it is not true!
So here I am, going crazy over a cat that I love to death, but can't stand anymore... Do they make sleeping pills for pets?