What can I do if my manager says I quit but I didn't?

Okay so today was payday at work and when my coworker went into work to get her check, the assistant manager told her that the general manager wasn't there and was holding her check, and my check, because she wanted to talk to us. So we weren't able to get our checks till we went back later. The night before she had called us and she spoke to my coworker and told her that if things were slow that one of us could go home. I specifically asked my coworker if she said one of us CAN go home or one us HAD to go home. She said CAN. So we both decided to stay. The other reason she wanted to talk to us was because we gave a guest (hotel) permission to park in a grass area because the lot was being repaved. The next day the owner of the hotel gave him a 24 hour notice but one of the workers called a towing company and had it towed. So my GM said that we had to pay them back for that. I didn't agree with either of those things so I didn't sign the write up. For one, I wasn't disobeying a direct order because she didn't say anything to me about going home early, and she told my coworker "can". That to me implies that we have a choice. Also, they had given that man 24 hours to move his truck. Another worker gave the towing company permission to take it even though he himself had put the notice on the vehicle. So I didn't sign it and she told me to clock out and go home. I thought I was being fired so I gave her my name tag and told her I'd turn my shirt in when I could. When I talked to my assistant manager she said that being sent home didn't necessarily mean I was fired. So I called the GM and asked her if I was let go or if I was expected to be at work tomorrow. She told me that I quit. I told her I never said I quit. She said that by turning in my name tag, I quit. I explained that I thought she had fired me, but she got upset, said "I'm not doing this with you," and she hung up on me. Can I file for unemployment? Is there anything else I can do?