You said she is your best friend (if this is the case, then it means it is a friendship worth the effort to save). If you don't want to say sorry first then don't, you don't even have to say it but it doesn't mean to give up on it (the friendship).
Let her head cool down and then take the initiative (go and talk to her first as if the fight never happened in the first place. This is what I usually do, I also give a kiss and a hug and act as if it is inconsequential because our time together is bigger than any fight.
However, after a while, when you think that this is the right time, talk to her about the things which bother you in her behavior. Don't be aggressive and don't criticize her .. start the topic by saying something along the lines of: I care for you and I become really upset when we fight with each other, what can we do to reach an agreement? I don't want to fight anymore or to make one of us upset? Perhaps ... [suggest a solution from your point of view]
and just be patient, it takes two to fight and two to sort it out ;)
Good luck
Ah I forgot to mention, use "we" when you talk with her instead of you or I (unless it is unavoidable) because you want to convey to her the feeling of a team work ... if you say "I", she'll think that you are only considering the issue from your point of view and if you say "you", it might sound as if you are criticizing/ blaming her which will make her aggressive.
This is just a suggestion, my way of handling fights ...
Thank you ♡ i will try and talk to her
Hey guys ,What should I do , my best friend and I have a huge argument right now and I know that she will never listen or say sorry, we been argue a lot, but this time it just her begin stupid blame other people. I gonna feel awkward cuz we have all 6 class together (even sit next to her) and this i don't want to be the person to say sorry ...:"(
Ps. Sorry for my poor English grammar