I had this very same problem with my Chevrolet Silverado. The only thing that will cure this problem is replacing all your Oxygen Sensors and running premium fuel.
Your Chevrolet Cavalier 97 might stall when going downhill because it has a bad fuel filter. It could also be the spark plugs misfiring.
Most likely a shot alternator, as far as misfiring it could be many things (bad spark plugs, clogged air filter, bad distributor, distributor cap) I would start with new spark plugs.
Bad plug or something is misassembled.
Bad plugs/coil/wiring
It is probably your spark plugs misfiring.
It is feeling silly and my other answer is it is behaving badly
Check spark plugs, plug wires, do a compression test
The Ignition Coil is the one that cause misfire or Spark Plugs
check spark plugs and coil pack
Check spark plugs and wires Do a compression test
8 spark plugs
check the coil pack