Water System Issue

I seem to have an issue only when we are on tank water using the pump. If we open a faucet to a moderate flow we only get a little water and when we shut the faucet the pump keeps running but with only a low noise. It just keeps running. If we open a faucet full blast and let it run a few seconds and shut it the pump makes a much louder noise but shuts off when the faucet is closed. The system runs fine on city water. If we haven't used the water for a couple of hours we seem to get a bit of air out first.

Before I begin to open things up any ideas where my problem is? I'm thinking it must be between the tank and the pump or in the pump itself.