You could have been an US citizen since birth. The only misinformed person here is your mom. She could have filed a Consular Report of Birth Abroad on your behalf when you were born in Australia. I'm afraid the time line was until you became 21 years old but I am NOT completely sure.
Research more here:
http://www.uscis.gov/portal/site/uscis/m…
The following has been taken from one of those links:
"Are you a citizen born outside of the United States?
The citizenship of someone born outside of the United States, as the child of a U.S. citizen parent, could vary depending on the law in effect when the birth took place. In most cases citizens born outside the U.S. requires a combination of evidence showing at least one parent being a U.S. citizen when the child was born and having lived in the United States or its possessions for a period of time.
To apply for recognition of citizenship, you have options:
Your Consular Report of Birth Abroad, or FS-240, provides proof of citizenship if your birth was registered at the nearest U.S. consulate when you were born.
If you are already in the United States, apply for a Certificate of Citizenship. Use Form N-600
Are you a naturalized citizen or derivative citizen?
You can use your original Naturalization Certificate or Certificate of Citizenship as proof of citizenship. If you have lost either of your certificates, you can apply for a replacement using Form N-565"
Having been a permanent resident 'til now qualifies you to apply for Naturalization so don't procrastinate any longer.
Is there a chance the law entitling you to become US citizen through her was not in effect at the time you were born? I have no idea but keep researching in the uscis.gov website (official site). It might only take a few more links here and there to look at in order to find a better answer to your question