[Indiana] I was just fired, despite my boss not being able to provide any documented examples of me violating company policy, or being able to list evidence of the reason she was firing. : legaladvice

So a few hours ago I just got fired from my job. I was a part time Mechanical Engineering intern, who was supposed to work from summer to fall, go to school in the spring, then come back for summer and fall. For the past week I've been having daily arguments with my boss over very minor and petty things. For example, she'd be upset that it took me a day and a half to make a training sheet for her instead of a day, or that I was doing projects for other departments (Small company with me being the only engineer, so its kinda expected). She would consistently accuse my of skirting around projects, despite me still delivering results every 1-2 days. During these arguments she would also do things that I believe were out of line, like pull out a phone and start recording me for "training purposes" or telling me "shit rolls down hill, and I'm at the top of the hill." She would also go to other departments and demand they stop giving me projects. The thing that pushed me over the edge was when she marched me into HR just to tell me that she didn't want a black outline around the text boxes on her training sheet.

During these arguments I'd lament about how shes extremely rushing a non-critical project (I know its non-critical because despite her demanding a day turnaround time from me, the completed sheets would just sit on her desk instead of going to the floor, which I criticized her for). I'd argue about how it wasn't her place to dictate what projects I can/can't accept, since my job was to help everyone in the company. Along this I reminded her that if the CEO or the CFO gave me a project, their projects would automatically get prioritized over hers for obvious reasons. Anyway after dealing with these arguments daily, I finally drafted an email to the CFO and the HR person about how I felt it was Harassment and I asked them to intervene. I had to ask one of the maintenance people about when a certain argument happened on a certain date, so I left the email on my desk and went to the floor.

When I came back my boss was at my office, and she just immediately says "I need to speak to you". She pulled me into the conference room, told me how we inherently didn't mesh and our relationship wouldn't get better, and that "I just can't work with you, so I need to let you go." She cited the fact she "couldnt work with me" as the reason for firing, but also that I skirted around projects (she couldn't list any examples when I asked for them). Anyway, there is no documentation of me violating policy, theres no formal reason as to why I was fired, there was no warning to me being fired, no disciplinary history, and as far as I know she didn't consult anybody else. While I can't prove she read the email that was on my computer, I have a suspicion that it was the reason for my termination. Basically my question is, can I fight this at all? Specifically could I claim wrongful termination? I dont have the employee handbook, so I dont know what the company procedure for termination is. Since I wasnt given a formal reason for my termination, I dont know what policies I supposedly violated.