1990 Cavalier bogged down.

I have a 1990 Chevy Cavalier 2.2
4cyl. I was driving to work the one
day when it started to bog down and
lose speed. It didn't matter if I
pressed the gas pedal any harder it
wouldn't pick up speed or stop
running bad. I pulled over, put it in
park, and turned it off. I let it sit for a
few minutes and started it again. It
started right up but ran like there was
no oil flowing through the engine. It
was bogged down and shook the
whole car so I just turned it off again.
Checked the oil and everything and it
was all good. I left it sit and came
back 2 days later to see if it would
start. It started right up and I drove it
home with no problems. I notice now
that it starts and shuts off really
rough though. I took it for a ride
today and it ran smoothly except
when I start it and turn it off. I don't
know what would have caused it to
run like that and why it seems
basically fine now. I don't drive it
around anymore because I don't
trust if it'll do it again or not. Can
somebody give me some clues on
what the problem could be please?