If you get fired from a job do you get something on your record?

Okay so i had a job during the summer washing dishes at a restaurant in a nursing home, and i gave them two weeks notice before i started school. They convinced me to do Modified Leave of absense, where i work every other weekend, the only problem is i cant call out and not work and i have to stay for 3 months. I have to go to work tommorow but i dont have any ride and i have a bunch of homework. how do i get out, or can i just quit suddenly though they always tell you you have to give two weeks notice. Also, if you get fired is there ever anything on your record, something a friend told me.