I hate to the the bearer of bad news, but your pump has cycled on/off until it no longer has any life left. When you take a shower or use water for any length of time a pressure tank system causes the pump to cycle on and off repeatedly. This not only causes pressure fluctuations in the shower but every start start takes life out of your pump motor. When a pump has cycled on/off many times the overload in the motor will start tripping. These overloads are auto re-setting and the pump just magically comes back on after a minute or three. Soon you will be standing there with soap in your hair and the pump won't come back on. Dip a little water out of the back of the toilet to rinse the soap out of your hair then replace the pump.
If you don't want this to happen to the new pump install a Cycle Stop Valve before the pressure tank. Not only will the CSV eliminate cycling and make your pump last several times longer than normal, but will deliver strong constant pressure to the shower which many people tell me is so strong they no longer need soap. Lol!
