A woman who brings up the past is simply trying to help you understand that you're making her feel the same way that you did at the time she's mentioning. Also any guy who understands women doesn't have to argue with them; but we're not perfect and that's why we're here.
Having said all of that, threatening with suicide etc is a huge red flag and yes, walking away is the best thing to do. Move on. Don't purposely make her chase etc because firstly it makes you the same as her, and secondly it's reaction seeking behaviour which is not only childish but it'll just increase your investment in her, hurting you when she eventually stops entertaining it.
Forget her. You got this
UPDATE: Funny, I went over and got the rest of my stuff from her today, she treated me like a total stranger, walked back in locked the door behind her then brought my stuff out to me and asked "so are you done?" wouldn't even look me in the eye. I replied with - I asked you a simple question and you can't give me an honest answer. She says "I need time" so I whispered "How much" couldn't answer that either so I said well, you know how to get ahold of me then and walked away.
Not more than 20 minutes later she is blowing my phone up calling and texting like crazy so I finally replied with a message about her holding grudges and treating me like a total stranger and let it go at that. Now she's sorry for "being a cunt" and feels like shit because I'm supposed to be her "best friend". Some best friend that treats you like a total stranger, right?
Maybe I shouldn't have replied at all but I was getting fed up of my phone ringing off the hook and all the messages. I don't think it'll be the last I hear from her and I bet she will try to contact me again very soon (if not again today), but I'm not going to reply.