1995 Chevy Cavalier Think its transmission Problem

Ight, I was driving my car and going about 20-30 mph and took a turn and went up a hill and my foot just hit the floor on the accelerator and I wasn't going anywhere! So I put the car in park and turned it off. Then I started it and it started fine, but when ever I put it in any gear, R, D any, it would just let me press the pedal all the way down and rev but I got nothing? Went nowhere! So I pushed it into a parking lot and I am confused on what to do, my dad said to look at the fluid levels for the transmission but I was wondering what happened or what it could be?