My water heater is not filling up, and none of the faucets have any hot water coming out

How do you know its not filling up? It may have water but noy heating it. Gas or electric, make model, and serial number would be a huge help.

"My water heater is not filling up, and none of the faucets have any hot water coming out"

If the water heater is not filling up then the water supply has been turned off. Check the valve at the top of the tank to make sure it is open fully. There is a tiny possibility that there may be a blockage in the line if you are on well water or live in an area with very high mineral content in your water supply. If the supply valve is open but you are not getting any water at the taps then try draining the tank to remove any sediment. Turn off the gas or electricity (or power to the fuel pump on the exceedingly rare occasion you might have an oil fired water heater).

Put a garden hose on the spigot at the bottom of the water heater and run the hose outside, then open the spigot to let the water and sediment flush out of the bottom of the tank. Let the water run until it comes out clear then shut it off at the spigot. Turn the power back on, or with a gas water heater turn on the gas and follow the lighting instructions on the tank label near where the gas line comes in. Check the faucets and see if any water is coming out of the hot water side. Keep in mind it will take an hour or two for the water to come out hot since you just drained the whole tank. If you are still not getting any water flow on the hot side then it is time to call a plumber.