I hope you are still talking to a counselor. You are right to understand that you can’t change the family member. All you can change is your reaction to her or your living situation. What the family member is doing is emotional and verbal abuse. It is enormously difficult to manage such continual abuse. Over time, it can wear a person down. As you found out, even trying to redirect the comments only invites more abuse.
I hope you are working with your counselor to figure out how to leave. This may mean temporarily taking a second job or even two to get the money for moving. (The advantage of working two or more jobs is it will also keep you out of the house.) You may need to find someone who will provide a home for your dog for awhile if that’s what it takes for you to leave. I hope you are also talking with other members of your extended family about what is going on. Someone may be able to give you a temporary home while you get on your feet financially.
You are in your twenties. It is time for you to figure out how to be an independent adult. Do everything you can to get out of this toxic situation.
I wish you well.