My problem is the relieg keeps on popping even when I shut down the hot water heater could it be a pressure problem since the water is cold? If so should I install a pressure reducing valve and if so what kind. Please provide any other suggestions thankks

It shouldn't do that.Sometimes they go bad or when it poped the first time it get dirt in the valve and its doesn't want to shut off Re purge it (flip) a couple of times Also look at the pressure gage of your water supply and see what it is. The pressure relief valve on top of the hot water heater should have a little brass plate to show what its rated or in pressure. They are easy to replace if you have to its just a new valve and some Teflon tape. Keep in mind the drip leg which comes off the pressure relief valve should be to the bottom or past the bottom of the tank for safety for you and the tank. Either way I would not trust it. New is good
Hope this helped Happy Holiday