I've got fired for no good reason. What should I do?

I've got into an argument with another employee. I asked her if she wanted to go get her break, but she didn't respond. I asked her again, but this time she yelled at me saying ,"GO,GO,GO!" I asked her what was wrong, and that's where the argument started. I didn't want to complain in front of the costumers because that would look unprofessional, so I told her if she wants to solve the conflict outside; not in a psychical way, but in a communicating. This happen two days ago. Yesterday they fired me. I explain to them what I really meant, and how this whole thing started. The manager didn't want to listen, or so it seems. I've been working for that company(grocery store) for 14 years, and they just tell me I'm fired. I've always gave it my best to give a good attitude and good costumer service, but it seems they don't care. Also, there was a witness (another employee) who was asked what happened. She told them it didn't look like I was threatening her. There's also customers who say she (the employee who I've got into an argument) that she has a nasty attitude when she's attending them. This new manager has fired many employees, too. What should I do?