You cousin is a bully and is abusive. It doesn’t matter that you are older. He is making your life miserable. I suspect that your grandmother is feeling so overwhelmed by “parenting” again that she can’t see the problems or is coping by trying to ignore them. She seems to be asking you, as the older kid, to do what she can’t. That’s not fair to you. You shouldn’t be asked to control your cousin when she can’t. You shouldn’t be asked to handle this alone.
I’m as worried about your cousin as I am about you. It is not usual or normal for a young boy to be behaving like this. I have to wonder what has happened to him that the only way he feels powerful is to be a bully. He is practicing patterns of behavior that are only going to make his life miserable too.
I’m so glad you are seeing a counselor. Take your letter and this response to your next appointment. Ask directly for help talking with your grandmother about the effect of your cousin’s behavior and what she intends to do about it. The counselor may be able to direct your grandmother to resources and a counselor who can help the whole family.
Hurting yourself won’t solve your problems. Talking to your counselor is likely to help all of you.
I wish you well.