Moving out to live with my boyfriend

Hello everyone, I'm a 20-year-old IT student and I would like to move out to try living with my boyfriend (he is 26 and we've been together for almost two years) and also learn to be more independent. Though my parents, especially mom, don't want me to move out saying stuff like I don't care about my family and that's why I want to move out or why did my mom buy such big house and as well that I said I will always live with them when I was 6 YEARS OLD.

Hearing those words from my own parents hurts a lot because I adore my family and I would do anything for them! I just want to try to be more independent and maybe have my own peace and quiet as well.

My parents are arguing every day (basically my whole life), fights where they call each other names and there are times where fights become physical from both sides as well. We are taking care of grandma, she is capable of walking but needs to be showered and cooked for and can't be alone in the house. I'm helping every day, that goes without a saying. I'm happy to help. Last year we were also taking care of grandpa (both moms parents), he wasn't capable of walking, he was a laying patient. Those were some tough times for my family, I also helped mom whenever I could with grandpa. Fed him, cleaned him up, changed his positions. Grandpa sadly passed away this April in our home surrounded by his family. Because of all the mess in my life and also because I wasn't able to process everything emotionally I couldn't finish my first year at the university so I have to start again in September. That's also a reason why I want to move out, I need peace and quiet to study and prepare for all the maths and informatics.

Now another reason is that my mom changed so much throughout the years. I love her, I try to help her as much as I can. But she calls me names. When something makes her mad she throws all the anger on me. One time it was so much stuff at once for me I cut my legs. I fell down so hard at that point of my life. When I needed to feel love the most she said she will give me a reason to commit suicide... Mom likes my older sister (she is 37) more than me. How do I know that? Because my sister would say the ugliest stuff ever to mom and my mom would do anything for her, mom doesn't call her names, mom isn't acting bored when she wants to talk with her...

I became this sad girl with no self-confidence, scared to talk because whatever I say at home I get punished for. I have troubles talking and explaining myself correctly. That's why I apologise if this was hard to read. English is also my second language, my "mother language" is Slovak.

I hope someone can give me advice on how to get through this situation, how to move out or whether I'm in the wrong for wanting to move out for reasons mentioned above.

Please, someone, respond :(