4 Answers

Credit cards are obtained with personal details, ask yourself "who" might have access to those details and go from there, ask your know it all sister?

Have you ever use it to buy anything on the internet??

Have you had no luck finding someone to represent you other than your sister?

First of all, you file a report with the credit card company denying that you made the charges.
They will do an investigation BEFORE requiring you to pay for the charges.
If you have never heard of the credit card, I don't understand how you could have used it?  But, filing the fraud paperwork should resolve the issue for you.  Just the address where the merchandise was sent (I'm assuming this was an internet use?) should be an eye opener.

For your sister to automatically assume that you are responsible and she depletes your funds without question is irresponsible of her.  Tell her, in no uncertain terms, that you are filing paperwork with the credit card company and she is, under no circumstance, to pay that bill until the matter has been resolved.  Shame on her for jumping to conclusions.  Bee-aitch.