I felt exactly the same at your age. I live with a single mum, older brother and younger sister (20 and 12)
I know it can be such a pain living at home with people who annoy you, bring your mood down and generally you just dont like being around
My advice would be to have some alone time, sit where its quiet or nobody is around, let everyone know youre working to keep the noise down and dont distract you (pretend its something hard)
One of the best things I have ever done is sleep at my nan's house around once a week, either a friday or saturday. Its great and get the house to myself on saturdaty night as nan and grandad go out.
That means just me music and sometimes even work
I really enjoy it.
I dont feel the same way anymore, and it just so happens im moving out in around 6 months!