You have the right to quit on the spot as most places fall under an "at will" employment contract, however, you are going to lose a reference and it does reflect poorly on you, even if you believe you have been wronged. There is an expectation of flexibility when you are hired somewhere so you have to accept some of it, such as switching departments, even if you "don't like" where you're moved to. The hours thing is another issue. If you were emphatic and there are reasons you truly can't work those hours that is something to confront.
I see you're only 16 and there are a few things that come to mind. First, I do have to agree that places tend to take advantage of easily exploitable groups. You being young, you're easy to exploit. However, refer to what I wrote above. There is an expectation to be flexible in some ways. You demanding to work only in one department seems to be a personal preference which I can't say I know exactly why but after managing a photo lab years ago imagine it might be because it's less work than cashing. I don't want to be presumptuous, however, but advice from someone who has worked since they were 12 years old and is now in their 30s, you get what you give. I don't recommend quitting on the spot, especially working for the company as long as you have. That's a good reference, especially for someone your age, you don't always see that with teens, they often jump from job to job, so think of what you would be losing before you make that leap. It may not seem like a big deal now but you have more than you realize. Just talk to them about the hours.