Q: Hi,Car started shaking when I put it in gear.it just recently turn off and when I put into gear.restarted car press down on gas pa

Hi,my car idle when it started and as I switched it into gear to reverse it shut right off.so in order get it back running I press down on the gas paddle and turn the ignition and the car came back on and while so it jerked again.im so annoyed no light notification has occurred ,so I could get a diagnostic.My inspection is due in a month and I really would like to have it fix.please help me figure it out I’m scared even drive the car down the road.i don’t want to make it worse. I put anti freeze in the back jug due to lack of engine coolant.foubd out back up jug was dirty while putting some in.so stop until can get back up jug flushed out.i couldn’t get the radiator cap to come off to put it directly in the car,so suggested to put it in the back up jug which is freaking filthy.

My car has 16000 miles.
My car has an automatic transmission.