OP, your family member sounds annoying and hateful.
This is one of those situations where you really have to be comfortable in your own skin. By that, I mean that you have to change your mind since you can't change your location. You have to figure out a way to not let their words affect you. Like others have mentioned, do not be afraid to remove yourself from all forms of communication, and be COMFORTABLE and CONVICTED in doing so. Realize that the household may be tense for a while, but it is for your own good (and it really is already tense, so it's not like you're missing out on anything)
Tell them straight up, 'don't talk to me, and I will not talk to you. Ignore me, and I will ignore you', go to your room, turn on your favorite song, and don't give a single 'eff' afterwards.
If you can't escape your physical prison, free your mind so that you can cope.
Oh, and lots of times people bring up a hurtful past because they see that you are progressing and doing good things, so they want to 'remind' you that 'you really ain't all that'. This is usually the case when you grow and develop, and they do not. You must be doing something right since this person is so hell-bent on hurting you and reminding you of how 'bad' you used to be.
Keep on keepin' on, OP. Good luck!