I suspect that the casing has a hole in it allowing debris to enter. To eliminate drilling a new well I would consider installing a cyclone type filter valveman will know!
Placing a liner in the well may be an option but it too is only a band-aid. I suspect that the particles are only coming from the cold water and not the hot water. If this is so, it tells me that the debris is settling in the hot water tank.
You can also install a 40 gallon galvanized tank between the pump and the pressure switch. The input from the well goes in the center plug in the side of the tank and out the top center of the tank. It may get you by for some time but keep in mind the pump is still pumping the debris, causing your pump to wear out sooner.