Should I see a psychologist?

My mom wants to take me to see one because I had a breakdown in front of her. I have been feeling worthless and terrible for about 3 years now around the time I started cutting. There are times where everything is fine in my life, but I will suddenly start crying. It doesn't matter where I am, I can be in school and I will just feel my eyes begin to water and I feel so bad for no reason. Then there are other times when I cannot focus on anything, I don't care about school work or friends, I just feel why live in this monotonous world? On top of that, I have these little breakdowns about twice a month where I feel so horrible I can't stop crying and I feel so desperate for a release I start banging my head, pulling my hair, punching doors, and cutting just to let out this rush of emotions. I also tend to have violent thoughts of killing people and the many different ways how to. I mostly have nightmares where someone is trying to kill me.

I just, I don't know, I don't want to go because what if all I'm feeling is normal and everyone feels like that, but they are really good at hiding it. What if I am just being a drama queen and they will say I am too sensetive or they will think I am really messed up and need to be sent away.

What are your thoughts on this?