If you have no separate shut off valve you should wait till the local water authority can come and temporarily shut off the water at the meter (which is presumably near the street).

I see no problem with shutting off the water supply to the water heater as a short term measure to curb the water waste from the leaking faucet in the shower. It would be a good idea to turn off the water heater during the time that the water supply is turned off.

After you turn the water supply back on the only issue you will have with the water heater is that some air could have fed back into the tank. All you have to do is to open the hot water valves in several of your sinks and let them run for a short while until the water runs clear without any bubbles or spitting coming out of the faucets.

There are three reasons a T&P valve opens. Temperature, pressure, or a faulty valve.

Temperature

If the water in the heater reaches a temperature of 210 degrees F, the T&P valve will open and release water until the water temperature is reduced. As water is removed through the T&P valve, cold water enters through the inlet and mixes with the water in the tank. When enough water has been mixed to reduce the temperature, the T&P valve will close. If temperature causes the release, there will likely be a lot of water released.

Pressure

Most T&P valves are set to open at 150 psi. If the pressure in the tank reaches this level, the valve opens until the excess pressure is released. If pressure caused the release, you'll usually see about 1 cup of water per 10 gallons in the tank (per release).

Temperature or Pressure

To figure out if the trip is being caused by temperature or pressure, you'll have to monitor both.

Test water pressure?

To test water pressure, you'll need a pressure gauge. They sell threaded gauges, that can attach to a standard hose bib. This will work well if you have laundry hookups.

1. Wait until the water heater is actively heating the water (you can expedite this step by using hot water, so go take a shower or something).
2. Connect the gauge to any hot water outlet, and open the tap.

Monitor the pressure through the end of the heating cycle. If you get a gauge with a "lazy hand", it will stay at the highest pressure achieved. That way you won't have to stand by and watch the gauge the whole time.

Test water temperature

To test the temperature, all you need is a thermometer.

1. Wait until the heater has just finished running.
2. Open the nearest hot water tap, and let it run for a minute of two.
3. Use the thermometer to measure the water temperature.

Causes and fixes

Without knowing more information about the installation, it's very difficult to speculate as to why this is happening. Determining why the valve is opening (temperature, pressure, or some other reason), is the first step to diagnosing the problem. Once you understand why the valve is opening, it will make it much easier to figure out the cause of the problem.