Problem with the stick shift

I have a standard Toyota Corolla 1996, with ~ 120000 mileage. I don't know what is its engine size (Sorry I am not much knowledgeable about cars).

The problem started a while ago as the stick shift getting stuck sometimes in the middle of driving so that I couldn't change to next gear. When I had an oil change the problem seemed to be gone away and everything was fine until it started again around the time for the next oil change. I hoped it to go away after the oil change but it got worse within hours after this oil change so that now the Minuit I start to move the pedal up in first gear the car jumps and afterwards the stick shift keeps getting stuck so much that I can't keep the car running and the car turns off again and again, so bad that I can't drive the car anymore. Can you suggest what might be the problem?