Nikolita
Family counselling sounds good. Or at the very least, you can sit down with them and discuss how you're feeling, and how it's affecting you. Maybe they can agree to stop fighting, or at least compromise and agree not to fight while you're around, or something like that.
I agree with Nikolita and Chalda... Unfortunately, it's one of those things that are easier said than done.
My mom and stepdad fight quite often. I hate it because my mom's getting on in years and I have to see how the stress in her eyes afterwards. She also fights with my sister like crazy. I don't care whose fault it is...but seeing them like that hurts me so much, though I don't usually show it.
I can also relate to your cutting incident. Recently, my entire family had this HUGE fight. I have a problem with accepting comfort from others...I also don't like to cry in front of others or have others know that I'm doing it. I was walking outside when I started crying heavily....I striked my arm with my nail (they're long and sharp) to focus my pain on that instead of crying. Afterwards, I thought about how stupid it was. I didn't strike my wrist because I knew, even at that point, that it wouldn't solve anything to cause myself to potentially kill myself: it's not worth it.
Telling my parents didn't help at all. They said what they "thought" they should say....but it didn't help. And counceling wasn't going to help my family either. While my mother is somewhat more conscious about how I feel when she fights...she doesn't stop. All I can tell you is that they won't ever stop fighting. It's going to continue. Yeah, it's scary when they do and you're going to always fear the outcome....but that's what makes times when you're happy together better.
After fights, try to do something nice...tidy up the house, wash dishes, make them a little treat without saying why. I do that for my mom sometimes...I'll go make her a bowl of icecream or someting, give it to her, smile and then just go about my business. Smal things like that help ease the tension afterwards. There are times my mom would ask me what its for and I'd reply, "just trying to bring a little happiness back in"...if I'm feeling smart with her, I'd add, "what with you and (insert) chasing what we had out" then leave. it gives them something to think about.
I don't know if I've helped...but I hope your situation gets better.