While running a bath in one upstairs bathroom, we heard an odd squealing/high pitch sound. Bath tub faucet was then turned off. Checked other upstairs shower and it was pouring out hot water, but in the off position. I turned the water to cold, turned the shower on all the way, and cold water came out. Turned it off, and the hot water continued to pour from shower. We've turned off the water in our house, as a precaution. But at a loss other than that. Any and all help/advice /guidance would be appreciated.

Thank you!

Describe shower valve. Single handle or two? Compression or cartridge type valves.

You should be able to turn off hot water by closing cold water input valve on water heater, then you you should be able to turn on main water valve to house. At least you will have cold water.

Yikes! Questions like this make me realize what a novice I am. By shower valve, I'm going to guess you mean the handle to turn it on (?). It's a single handle. First, we turned off the hot water valve, and then the main house one as it's evening and water isn't required.

A single lever valve would be a cartridge type. Problem will be in the cartridge itself.

I repeat you can turn off all hot water to the house at the water heater and still have cold water.