When one member of a family is suffering, everyone suffers. Your parents are doing their best to love your brother through whatever this “rough patch” is about. Because they see you as the healthy one, it may be that they have lost sight of the fact that you’re only 18 and that you are suffering too.
A couple of thoughts: First, you can’t convince your brother. You can’t make him take care of himself. You can’t make him see your point of view. He’s in the grip of whatever is troubling him. All you can do is tell him clearly that you won’t stay when he loses it and that you will leave. Then do it. Go to a friend’s house. Go for a walk. Go do something that is healthy for you.
Secondly, when reading your letter, I wondered if anyone has asked if your brother is drug-involved. Sometimes what looks like mental illness is actually caused by drug abuse. If this hasn’t ever been talked about, maybe you can encourage your parents to check it out.
Finally, however much you want to help, you and your parents can’t make your brother get treatment. You can go to family therapy for yourselves – and you probably should. You all need more support and you could probably benefit from talking to someone who is experienced in mental health issues both to figure out what is going on and to decide how best to handle it. The counselor can give you some practical advice about how to support your brother and how not to lose sight of the needs of everyone else in the household. Ask your family doctor or another professional who knows your family for a referral.
I wish you well.