1997 Chevy Cavalier oil pressure light

It could be a bad oil pressure sender, or the oil pump pickup may have worked loose.

I would change the sender first, if problem persists, remove oil pan and check pump pickup.

Normally I would say it was a faulty oil pressure sender, but since you say it goes off when you accelerate, it sounds more like a oil pump pickup in crankcase.

Oil pressure sender is on left rear of engine, remove connector, clean and reconnect, if problem persists, have oil pressure tested with mechanical gauge, if OK, but problem persists upon stopping and acceleration, then oil pump, or pickup, or possibly the oil pan baffles are bad.

The question of cost vs. value of car is a question only you can answer.

If you do the work yourself, you maybe looking at $400-500.

If a shop has to remove pan and oil pump, then double the cost.

If it is a bad gauge sender, then nothing would happen.

If the oil pressure is in fact low, you will starve the engine of oil and eventually cause premature bearing failure, main and cam bearings in particular.