If you sister had informed the council that you are a student and that she was the only non-student adult residing in the property, the council may have given her a single occupant discount (because a student does not count for the purpose of council tax).
In the above case, your sister, as council tax payer for the property, should inform the council tax department that you ceased to study at the end of whatever was the end of your academic period. They will then recalculate the council tax bill and let her know what the new council tax will be.
As mentioned above, council tax is paid per property and not per person (look up Poll Tax riots and the history of the Community Charge to learn more about that). So you will not pay a separate council tax.
If your situation is different that the one above, you may want to take the query to the local
Citizen Advice Bureau, because it is not an immigration issue, but a local tax issue.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.