I'm thinking of potentially ruining my relationship with my brother by choosing to live in a dorm
I am not sure I understand the basis of your thinking. Why would you ruin your relationship with your brother by living in the dorm?
I want to have my own life and live in the dorm.
It's okay to want to live separate from your brother. He should understand that. You are an adult now.
I don't want to live with him anymore and I want to be independent. I will tell him that I don't want to be near him anymore, it's too uncomfortable.
I think you are doing the right thing. Your brother should be happy that you want to know how to be independent in life.