Do I Have Social Anxiety Disorder? My Mental Health Struggles - Psychiatry

Does this qualify as a mental illness?

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Hello, doctor.
I have two personal issues I would like to seek help with.
Thank you!
The first issue is that I have been very shy since childhood.
In kindergarten, I was unable to speak to my teachers or classmates, not even a single word, which led to me being seen as an oddball and having no friends.
It wasn't until first grade that I could speak very softly and made one friend, and gradually I became more normal.
Now, in my second year of high school, my interpersonal relationships seem fine, but I feel extremely anxious and fearful every day while taking the MRT to school.
I don't know where to put my hands or where to look, and I experience intense nervousness and fear, sometimes to the point where my legs shake.
I also dread shopping because the clerks are strangers.
Every time I have to buy something, I have to mentally prepare myself extensively to manage my fear.
Am I suffering from what is known as social anxiety disorder?
Secondly, I come from a completely patriarchal family.
I am closer to my mother because I resemble her, and my parents have a poor relationship, leading my father to favor my sister.
Since I was two, my sister has brainwashed me, telling me that I am the ugliest person in the world and a freak, and I believed her completely.
Later, she began to exclude me with other children, telling them I was a freak.
Whenever I was bullied, my father would laugh and watch, finding it amusing, and would even help my sister bully me.
If I cried, my father would say I was narrow-minded, couldn't take a loss, and was combative.
I harbor a lot of hatred towards my father and sister.
When I was three, I dreamed of killing my sister by stabbing her throat with a sharp object, with my hands covered in her blood.
Our relationship improved significantly as my sister grew up, but my father's perception of me did not change; he still sees me as combative and self-righteous.
Last year, when I got into my first-choice school, I excitedly called him to share the news, but he skeptically asked if I was sure and then said he had to teach my sister math before quickly hanging up.
Later, I overheard him mockingly tell my mother, "It won't matter; she'll definitely be at the bottom." My father seems to have a mental illness; he wakes up screaming several times every night and has social issues, often suspecting that others look down on him and frequently getting into arguments with strangers.
When he is angry, he exhibits violent tendencies, such as choking me, slamming my head against the wall, tearing my clothes, or dragging me by my hair on the ground, as if he wants to kill me.
He also throws cups and flips tables at me, my mother, and my sister.
He uses degrading sexual language to insult us, such as when I wanted to go to karaoke with classmates that included boys, he called me a "whore" and said I "wanted to be used." These incidents continued even into high school, and I have completely lost trust in him.
I have to lock my bedroom door at night to feel safe.
When I hear him come home and open the door, I immediately rush into my room, no matter what I am doing.
If he yells at me, I become so agitated that I lose all rationality, shaking all over and uncontrollably breaking things with immense strength, shattering hard objects, and then crying, screaming, and shaking for at least two hours before I can calm down.
I feel extreme panic and anger, imagining him coming to kill me and my mother and sister going insane from the trauma.
At the same time, I feel intense hatred towards him.
I become so frightened that I curl up in a corner while also feeling furious enough to want to stab him.
Am I suffering from a mental illness, and is there a way to improve my situation? I am very afraid that during my outbursts, I might do something terrible...

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Joyce, 10~19 year old female. Ask Date: 2015/09/28