Gosh, so sorry to read about what you've been going through with your uncle and cousin. It's hard enough adjusting to a new living arrangement, let alone figuring out how to deal with arguments.
In a perfect world, our homes should be a place to rest and recover, which I can imagine is pretty hard when you're on edge waiting for the next debate. Even though the response isn't what you hoped for, good on you for communicating your needs and boundaries to your cousin.
I know you've posted in the past about tough times at home with your dad and sister, and when I put myself in your shoes, I get the feeling this situation with your current living situation would be extra upsetting. I'm curious to know what your relationship with your aunty is like. Is this something you could confide in her about?
Also, I understand your thoughts about wearing headphones, but if you ever feel you're being pushed to your limits, I think this is actually a great way to get some space and look after yourself. I'm not sure if this article about conflict with family will have tips that resonate with you but I thought I'd share it in case.
Hope you're having a good day!!