Hey there,
I'm sorry for everything you're going through with your boyfriend's brother. From what you've said, it sounds like his brother is very unreasonable and really does not like you. You say that your boyfriend always sides with him. Can you think of any possible reason why? Apart from the fact that they're family?
You could try talking to him about it and how it's affecting your life and your relationship. There's no reason for you to leave your own house when someone else is being unreasonable, but perhaps if you and your boyfriend really sat down to talk about it, he might be able to provide you with a better explanation for his actions.
And if it still doesn't work out, then perhaps you might be better off not being in this relationship. If he cannot defend you in obvious things like these, then maybe it's a sign that your relationship might encounter problems if it continues on.
But again, this is all based off of what I gathered from above.
PM me if you ever need to talk!
Kyra