Part time job not a good fit, should I quit to look for full time?

Megan, I can certainly understand why you'd want to get a job in your career field. However, jobs are hard to come by right now so unless you could make it without a pay check for an undetermined length of time, you should look for another job while still working at this one. When you find another job simply tell your employer you've found a job in your career field - after all that's why you went to college. If you do leave this job before finding another one tell the potential employer you wanted to get a job in your career field and didn't have time to look while you were working. Until then I'd ask why you and the others are required to finish up your work after you've clocked out. They can't legally require you to do that.