Hot water valve not working
If you have access to your water heater, it will typically have a shut off valve on its entrance to allow being serviced.  If you can shut that off, that will kill the pressure on the hot water line, and you should be okay.
Open the hot faucet to confirm.

Given that, I would consider taking that shutoff apart and fixing it if you can.

Probably a worn out or deteriorated rubber washer.  Worse case if that is just attached to the plumbing by the nut behind it, you can replace the whole valve.

Take it with you to a store.