Well pump stutters and hesitates then shuts off and lights in the house flicker

We were away on vacation and came back to our well pump making strange noises when we used the water. It stutters, hesitates, then shuts off. In the meantime, all the lights in the house flicker. I cleaned the contacts, added air to the tank and cleaned the pressure line. All to no avail. Pump is still making noise and lights are still flickering. Any suggestions?

There's not really enough information to diagnose your problem but by the lights flickering when the pump is running tells me that you have an electrical problem. If the pump has a control box, the problem could be a capacitor, or relay in the box. To prevent damaging the pump motor you need to have it checked by a qualified pump man ASAP.