Two things...water expands when it heats, if there's no place for it to expand into the pressure will increase - often high enough to trip the T&P valve which brings the pressure back below the trip point. And, your plumbing doesn't like really high pressure - hoses can burst, glasses can be shot from your hand when filled under the faucet, but you can get a great shower! Since the copper pipes don't expand much, just a little water expansion can raise the pressure a lot, just like dumping just a little water can bring it back to an acceptable level. Most places highly suggest a PRV if the pressure from the street gets above 80#.
If you have a pressure reduction valve, it sounds like it is shot. Some can be rebuilt, but it is often about the same to just replace it with a new one.
Some water meters have a check valve in them, too. So even if the pressure is normally acceptable, when you use a lot of hot water, replacing it with denser cold, when you heat it up, it expands and can give you grief unless there's an outlet for that increased volume.
If you know how to solder, adding an expansion tank isn't a huge job, and the parts are relatively cheap (in the $50 range for tank, tee, valve, strapping to support it, etc.). A PRV would cost more in parts, if required.