At the first sight one might think that I have a great relationship with my mother. I tell everything to her and listen to her advice. She's very progressed person and I find many things in common. But I see that she has a big trouble with herself and that's why she is messing up with me all the time. I am already 18 years old and having a freshmen year at University. I have thought about moving from my house to get rid of such problems with my mom. I live in Georgia and it is hard to find part-time job. That's why I have to handle all the mess.
She has a tensed relationship with her sister, who lives near us. Even though they never fight and formally have normal friendship, she's always telling me how her sister treats her bad and how she's heartbroken. My mom would never tell her sister what she really feels towards her and that's why she directs all the anger on me. My mother hates that I have a close friendship with my cousin (my aunt's daughter) and every time mentions my relationship with her. She thinks that I don't listen to what she says and than starts to fight (very seriously). She can get mad about small things. It develops in insulting me and saying nasty things about me. Days pass and we don't talk with each other. That's why I hate coming home.
If there's anybody who can give me an advice, please help me to work things out

I don't know what a "progressed person" means.

Have you tried counselling? What does your aunt say about the situation? She's (presumably) the other half of the argument.

Is your mother trying to "dictate" your friends and trying to keep you from contacting your cousin?

The bad part of this may be that as long as you live in her home, you live by her rules.

I mean she thinks like people of my age.
I tried Counselling with my father. He also finds hard to make her happy or pleased. He knows that she exaggerates her emotions and tries to carry all the anger on me.
My cousin is not the only argument of her fight but I feel that every time she sees me with my cousin or comes back from my aunt house she is strained and ready to burst out. Than she starts to fight even about a table dusty.
Fortunately my brother found the way to evade her. He hardly ever communicate with her when he's at home. But she has a close relationship with me and that's why I become a victim

We have someone here I think can help you - let me ask her to join "us."

Yes, it sounds like you are the target of her anger.

I'd suggest that you make sure your mom knows you love her - going to college and wanting to be out with friends and more independent, she is probably jealous of time you spend with other people because she feels she's losing you.
Also be sure to express your appreciation to her - for making it possible for you to go to college, for making a holiday special, etc. She may need to hear things like, "it's so great - you're the one person I can talk to about everything".
YOu also will need to establish some boundaries - carve out some time and space for yourself. As an adult, you don't have to disclose to anyone all that you do and all the people you do those things with - you don't have to tell your mom every time you see your cousin, for example, if it upsets or makes her jealous.

As for her relationship with your aunt, I think you'd best stay out of it. Be supportive to your mom, perhaps encourage her to get counseling and/or work on the relationship, but you can't fix it.

Your mom needs to work through this on her own - you can offer support but can't fix it.