Should I quit my job?? Am I overworked and underpaid?

I'm a college student and work part-time as a preschool teacher/day care worker. There is great controversy regarding the high ratios....All of the classrooms have high ratios (Ex: one teacher for 12 four-year-olds, 1 for 8 2.5 year olds, one teacher for 4 babies.) Plus, they constantly switch kids around from room to room at the end of the day to maintain highest ratios possible. Anyways, today I was working in the infant room (I don't normally work there) and so I had 4 babies to take care of. I was switched to another classroom for about an hour when my co-worker told me that baby Ryan had a scratch on his face (It was a little tiny scratch). She asked me how it happened and whether I wrote an incident report. I actually think it could have happened when another teacher was in the room (we have several teachers in one room each day bc we constantly switch). However, I panicked and took the blame for it because I was nervous. My co-worker went and got my boss and complained to her that I didn't write an incident report and said how awful it was that I didn't know what happened. My boss was very upset with me that I didn't know how it occurred. I became nervous and suggested maybe another baby scratched him. The boss said babies don't scratch each other. I'm mad at myself now because I honestly think it must have happened when I wasn't in the room but I became nervous and falsely confessed. And the thing is, the parents didn't even care about the scratch. They just said "oh okay" and said good bye like normal.