Wow, it sucks to be to your situation, i hope you're okay =/
But in terms of appealing, you should definitely do it.
I'm not sure how it would work for your school, since some schools might just base getting extra marks on your previous results, so if you haven't done too well, it doesn't help much.
But in other situations, they might be more lenient and give you a few extra marks because they realise your situation has genuinely impacted you.
I think the best thing to do is to go see someone like your year adviser, or welfare teacher straight away, and then they can refer you to the school councilor.
And going to the school councilor would not only hopefully help you get through it, but they can also play a massive part in backing you up if you want to make an appeal, because it makes your case more legitimate, especially if you've been deeply affected.
& appealing can extend to the hsc as well.
This is a bad example, but i know of a girl from my school a few years ago whose parents faked a divorce just so she could get extra points, and she ended up getting 5 atar points, consequently getting into usyd law.
All the best, stay strong!