I have to agree with turnandburn.
Why have you only put your child's name down 2 years prior to starting school?What were you doing for the 2-3 years earlier? If you have been here for 10 years you should have known that schooling is an issue and to put him/her down as soon as possible (as soon as they have a birth certificate).
I do feel for your situation, but it is through choices you made. It's not the AOA's fault. Although , maybe as part as a welcome/new joiners pack, it can be emphasized how hard it is to get children into school in Hong Kong and use your case as an example.
Good luck