[Jmrec100]

Any trouble codes? Check engine light?
I have a 1999 Cavalier. There is a speed sensor mounted passenger side under the Half axle drive of the trans. Yours is probably mounted somewhere else. Look for it. Prior to my engine blow-up, the oil change place disconnected it. Why? They said so they can get the filter. Yeah, right?
Anyway, my car behaved like you say. I reconnected it and was fine until found they messed with my PCM too. Reason for my headache I have now. Can't prove it but never going there again. Went once a month for my car and the normal 3 - 4 months for my wife's and kids. I tell everyone I know to stay away from EZ lube. Not the first time they messed my car. Left the over flow bottle cap off and closed the hood. Nice round circle where the cap was. I drove across the driveway and parked. Saw it. I lost it with them. Also previous things too.
So that's how I know to Look for your speed sensor. Probably disconnected or came loose.