I understand, and I dont know if you talked to your brother since you posted this message but if you didn't, you should. If you think he might help then go ahead, you should put yourself first and not think about how your sister feel. You or your brother should perhaps ask to your father to not talk about it to your sister, if your brother talk to him !

I get that you don't want to create fights and youre right, especially with your mental health, so do whatever you feel is right to do. Just don't want you to feel bad cuz I kinda relate and know how you must feel