I think I was similar - I definitely had a fear of failing and disappointing everyone. But you have to take a step a back and remember that you have to be doing the HSC for yourself. In the end, it's your work you're putting in, your marks, your ATAR. No one else's. I know the pressure can get a bit overwhelming, but you have to remember that if you disappoint anyone, it will be short term. If you get to the end of the HSC and know that you've done your best, then that's all anybody can ask of you. If they're disappointed, then they need to get their priorities straight. I've learnt that by the time you get to the HSC, you're old enough to take responsibility for yourself, you are no longer a kid that has to please your parents or anything. The HSC is about independence.
Also, do you have an ATAR goal/degree you want to get into? If so, stick it on your wall or something, to help you remind yourself that you're striving for something you want. When I was going through, my parents didn't pressure me exactly, but getting good marks was just expected. About halfway through the HSC, I'd really had enough of it, so I stuck my goal ATAR and course on my wall and told myself that I was now working for myself and no one else. If I got a 'bad' mark (according to my parents), then it would still get to me, but not as much as before. Also I think it's a good idea to talk to your parents - tell them everything you've said about your anxiety - let them know you're working for yourself and no one else.
I think it's also a good idea to not tell your parents your marks when you first get them. I know that sounds weird but I told my parents I would do that because I wanted to teach them that my ATAR didn't define me and it was mine. I told them eventually, but it did teach them.
I hope this helped - if you have any other worries then don't hesitate to vent! Remember that everyone gets anxious. But I think once you start having a positive attitude and a mindset that you're working for yourself and you alone, then I think you'll have a different motivation - not an anxious one, but a drive to achieve what you want.