Should I do something about being fired?

I used to work at an ice cream shop run by an older lady. One night, my coworker and I were closing the store. My coworker was in a hurry to get to a date she had after work, and she was rushing the closing procedures very much. Every time I attempted to do something, she’d take over and tell me to go do something else. It was very confusing and chaotic, and I tried to make sure everything was done correctly, but we forgot to set the alarm when we left, and my coworker told me that we needed to set the ice cream machines on a setting that was incorrect, despite my belief that the other setting was the right one. My reasoning for going along with her belief was that she had worked there long before I had been hired, and had much more experience closing than I had. So, the next morning, my boss called both of us, and my coworker was in town and would be working later, so she would talk to her then. However, I was out of town for the weekend, so my boss began the conversation about what occurred the night before with me via telephone. I explained the circumstances to her, but I chose not to bring up my coworker’s date plans, because I felt them to be too personal and irrelevant. My boss’s temperament changed as we continued the conversation to more agitated, and she told me that since I am older than my coworker (I’m 20 and she is 16 or 17), that I should have known better. After she told me this, she informed me that it was not going to work out, and fired me. This is just the tip of the iceberg as far as the unprofessional and inappropriate things my boss said and did while I was employed there. She said many sexist things as well. Should I write to the corporate center of my company or do something at all? Was what happened even fair?