Any transmission advice?

After i let my sister drive my car (which im never allowing Again), ive noticed that whenever my 1990 automatic toyota celica trys to accelerate from 0mph to around 35-45mph, it slips and shakes, the speedometer also shakes. i usually just have to push the pedal hard then it jumps to 3rd gear and im fine. but it also does it when ive been driving in a low gear for awhile then when i try to accelerate it starts to shake, then i press the over drive button to help it. if you have any advice like how long my transmission may last, please tell me, thank you.