1988 Oldsmobile Delta 88 Engine sounds / car shakes

I drive a 1988 Oldsmobile Delta, and it has been running great for a long time. About 5 months ago the car would make a "clicking sound" while I would drive or sit idle. When I rev the engine in neutral or drive, the sound would stop, but only return again after I released the gas pedal.
Most recently, the car now makes a very loud clicking sound, and is actually "coughing" when I drive, almost sputtering. As soon as I start the car it shakes hard and then just a little, and will persist throughout the drive. The engine now really makes a loud clicking sound, as is a nightmar at stop signs and red lights. Also, when I accelerate the car will drive for a moment without shaking and then shake REALLY HARD, causing me to let go of the gas and then press it again, as if to let it get a second to relax. What's the problem here? Any thoughts would be appreciated.
There is no fluid dripping, no smoke, and I did not hit or crash into anything.