So my bathroom sink faucet is leaking at the faucet and soaked everything under the sink. i was trying to turn the main water lines off that go up to the sink but the hot water know broke. how screwed am I? what do i do now?
Can you not take a screwdriver and turn the screw at the knob that broke to the off position? This could work at both the faucet knob and the main knob from the wall.
Assess why and where the knob is leaking and you can pretty easily fix it or better yet, buy a new set and install in minutes. Get some plumbers tape or glue and a flashlight as well as proper tools.
I assume you found an answer by now, but the correct answer is to turn off the water to the entire house. There is a shut-off valve out by the meter, which may be between your house and the neighbor's, but it is out there somewhere. Get that tap turned off, then you can disassembly the broken shut off under the sink and take it to a plumbing or Lowe's store to get replacement parts.