I think that if you are 16 then there shouldn't be any issues with respect to your records being confidential from your parents. I know that I had therapy when I was 16 with drug and alchohol services and my parents didn't know about that at all. That was NZ, but I'd imagine things would be similar between NZ and Australia.

Why couldn't you return to the therapist you saw? Can your school counsellor refer you on to see anyone else?