The first step would be to call in someone who knows something about pumps. Normally, pump range is 40-60 lbs. or somewhere in that range. You've got far too much differential.
Another help would be a larger tank, and it's possible that your tank is no longer functioning well - the pressure tank should be checked for correct base pressure.
If you have a pressure-balancing faucet in the shower, chances are the pressure variation is more than it can handle, or you're getting an initial surge from the pump when it kicks on.