I had a fight with my really good friend? Should I apologize?

So I have this friend who's one of my best friends. She is the kind of girl who gets offended by little things the no one is getting offended by and takes things to heart.

So we had E.D and we both hate it (one semester is Gymnastics and the other one is volleyball. We both hate the volleyball semester, which is now), and she kept talking on and on about how she hates it and I got pretty annoyed and told her "Okay, what do you want us to do about it?!" and then I saw other friend of mine and told her hi and then I see my friend like storming-off walking and I called her but she just kept walking. When we got to class I asked her what happened and she said nothing, never mind. So I left it.

Then when the class ended (it was the last period) I asked her why she stormed off and she told me that it was a rude thing to say and she said after I told her that "thanks, May" in a sarcastic voice and I didn't answer her so she walked away. I told her that I didn't answer to her because I just saw my friend (what, she wants me to ignore my friend because she got offended??) and she wouldn't listen to me.

I told her she's over reacting and then she told me "It's like when you said to me you cut and I would tell you 'so what? What do you want me to do about it?'" in the annoyed voice I told her. And when she said it I yelled "It's not the same!" and I looked at her for a few moments, and then walked away.

I used to cut and my parents found out (I stopped if you wondered). I don't know why I even told her.

I was hurt by what she said. I mean it's a completely different thing! It doesn't even... how could she compare it to this?? How could she use it as an example or a comeback in a fight? How could she use it against me?!

I was over sensitive about it because last night my mom did another lecture about it and I just can't anymore... I am hurt by her.

Am I over reacting? Is she right? What should I do?

I was going to apologize for her before she said it, but now I don't really want to see her...