Questions about home water pressure (105-110 PSI range) and the drastic pressure drop when a single faucet is opened
It sounds like your pressure reducing valve (regulator)  is not working properly. 
Normally the max pressure is 80 psi or less, there are several possibilities since this was not a problem in the past we will go to debris plugging the orifices. I have found that rust / scale has prevented the valve from fully closing thus you see full pressure at all times static, once there is flow the valve opens but the orifices are partly blocked so the flow is limited and the pressure falls.

Hopefully you have a shutoff valve prior to the valve / regulator turn the pressure off bleed the water pressure off and back the adjustment. now disassemble  you will see several small channels and the debris are probably obvious, I put a rag over the body and turn the water on for a second to flush other small bits of crud. I clean the diaphragm and reassemble (if you can find a rebuild kit these are a good idea incase the diaphragm gets damaged) the last kit I bought was mid 20$ some are less depending on size and type. Make sure to get a potable kit since this is a source of drinking, bathing and dish washing water. 

Once reassembled or possibly replaced turn the water on and increase the pressure setting to the 60-80 range (this is normal fro many homes) now when you turn on a faucet the pressure should stay at or close to your pressure setting.

The one thing I did not talk about was a ruptured diaphragm but these normally have full flow because the water bypasses the valve section through the rupture.