Dripping T&P valve with ExpansionTank

After repairing a leak in my water softener, the T&P valve on the water heater began dripping. I replaced the T&P but it still leaked. I put a pressure gauge on the water heater drain and it showed 150 psi. There is a pressure regulator that was already installed in the system when I bought the house 15 years ago. I have an expansion tank that was installed when the water heater was replaced 5 or 6 years ago. If I run water anywhere in the house, the pressure quickly drops to about 60 psi but just as quickly builds back up to 150 as soon as the water is turned off. Right now the pressure regulator is my chief suspect, but I don't want to go through all the work of replacing it until I am fairly sure that is the problem. My understanding is that the regulator only has an effect while water is flowing. I've been told that since the pressure builds up after the water is turned off it is a thermal expansion problem (BTW, the pressure goes to 150 psi regardless of whether the heater is heating or not. It is a gas heater) but I already have a thermal expansion tank. Any suggestions or advice would be greatly appreciated.

If the PRV is 15 years old, it may need replacing.
The pressure shouldn't build up right away.
It would be gradual, and what little expansion you had would be served by the expansion tank.

Just a suggestion, when you replace your PRV you may want to consider replacing your Expansion tank also. The tank should be precharged to the same pressure as what you set your pressure on the PRV after installing it. Like everything else in this world, the tanks don't last for ever. It may be the easiest plumbing repair there is.

Test?

Thanks for the replies.
Is there any way of testing the PRV or the expansion tank to see if either one or both need replacing?

Yes...you can buy an inexpensive (less than $10) water pressure gauge at one of the big box stores, or a plumbing supply house. It will screw onto the washing machine hose connection, an outside faucet (caution, this may be connected before the PRV, so it won't give you the reading you want), or you can buy adapters and screw it into a faucet through the aereator socket.

On the expansion tank...tap the thing to see if it is full of water. If it is, it is probably bad. Also, unscrew the cap on the air valve (just like on a tire). If water comes out, it is shot. If not, then use your tire pressure gauge to check the pressure. Note, if it isn't leaking water, the air pressure will be the same as the water pressure.

The tank should have a pre-charge in it equal to or slightly higher than the normal water pressure. To do this, you need to shut off the water, open a faucet to relieve the pressure, leave it open while you use a hand pump to pump the tank up to pressure.