A couple of things: first, you can pick up a screw-on water pressure gauge with a second (tattle-tale) hand to show peak pressure at any plumbing supply or big box store for around $10 or so. You can get one that will screw onto a hose bib (maybe the drain on the WH, or the washing machine connection, or with adapters, anywhere). Pick one up and check. Any reading, either peak or static above 80psi requires a PRV... the PRV from the factory is probably set at about 50psi, but it is adjustable.
The relief valve may just be doing its job. If yours really is adjustable, you could try raising the opening point.
A home with a PRV should also have an expansion tank or as in your case, with the pressure relief valve, wasting a bit of water each time the WH ran after hot water useage. While a PRV can be serviced, since that doesn't always fix it and labor is expensive, it's generally better to just replace it when it fails. You don't need that relief valve, but it doesn't hurt. If the PRV and expansion tank are working, that valve would never open. It is a second, or third, depending on how you look at it, means of maintaining pressure: the T&P on the WH will open if the pressure gets to 150#, the expansion tank (when present and working properly) will prevent the water pressure from rising as a result of heating water, and third, that pressure relief valve, which may be gummed up and now stuck open.
In the interim, you might just cap it. I'd consider picking up a Sharkbite cap to limit your water wastage until you figure out the rest. Those are easy to install, take no tools, and can be removed fairly easily. You do need either their tool (it may come with it), or a pair of pliers or a wrench to compress the latch so you can remove it.