Actually am also confused about the relationship and difference of engineering computer science, Information Technology and BSc in Information Technology. By reading the thread some points are cleared now.
I think as the cem says you have to choose on from Math and English because of a school's rules and regulations. You can accept one which you have more experience and interest in teaching than other!
There is lots of career options after doing the science degree like you said in Physics and maths.
You can get a job in engineering field and also you can work as a teacher in a University.
Research Mathematician is also option here.
From my opinion it is better to choose USyd if there is a good IT department and helping teachers.
If you do work hard nothing is bad and your success is 100% sure.
Best of luck for your better future!!