it's awful to hear, but unfortunately sounds far too familiar.
My dad's an abusive alcoholic, both sober and intoxicated. My mum denies he's done anything wrong. My brother and my sister have succeeded past this, but I've found myself, at 17, unable to, slowly my concentration has deteriorated and my dream of working in medicine is reaching further and further away. My brother and sister refuse to acknowledge there's a problem, 'if they can succeed, why can't I?' it's something they and my mother believe I've chosen. I have no friends.
I think what you really need is support, and if not from your family. Go out, I envy your ability to spread yourself to somewhere beyond your own front door. Go out, engage, sure you can't lay all the heavy on someone straight away, but you need to find someone you can idly chat to <-- i found I got worse when i lost my only friend and cause I spent so much time with her, my strange thoughts and problems came out so subtley over a larger space of time, which I have only discovered reflecting back on it.

If you're family don't understand, don't waste your time defending yourself. Sure you love them like anyone would their family, but someone else deserves their time with you. YOU deserve your time better spent.

You should be seeing a pych, they're good guides. But most importantly, you need social support. You are rational, trying to work with irrational = you'll become irrational (and you are....you indirectly described it in your posting)

good luck