Can I randomly chat with her or do you think she is still really mad?

[Ladiesman122]

Me a guy (17) and this girl (15) were best friends since last Novembor up until May. We were the best of friends and told each other everything and had so many inside joke and we basically loved each other like a lot.
We got into this stupid fight over Facebook, because a friend of hers started a fight with me and I finished it. She told him to be nice to me as we were best friends, he didn't, then She freaked out on me and said I was being mean. I retorted and we basically swore at each other over her status. *Things got bad and she limited her privacy setting so I couldn't comment or write on her wall. I was really hurt so I defended her, but immediately felt really sorry and I re added her.
I apologized sincerely and I noticed the whole walloped thing was lifted. I tried many times in May to apologize over text to find out she lost her old phone and got a new number (this is legit) she said she accepted my apology and we talked somewhat normal on chat, but then she got so cold on me one day and stopped at all. I talked to her boyfriend who everyone hates because he's an a**hole, but were ok and he said well shes ignoring you because apparently you said something to her friend not nice, but said she will talk to you like next week or something. That week came and gone and she stopped noticing me at school. I went to her locker and decided to tell her how sorry I was and tell her how I felt, I asked if we could talk. She had this cold hurt look and almost looked like she wanted to cry and said "no it's ok" so I just walked away forever or until now. I've missed her to death but have Long got over her as she meant a lot to me. Just last week I was at a mall, and I was sitting down texting someone and she and her friends passed me and she kind of slowed down and gave me this dirty look, I didn't even notice it until she was gone and my friend nxt to me told me about look.. Can I randomly open chat window with her on Facebook? Asking "hey, are you still mad at me"? I need help and yes facebook is the only form of communication it's complicated