Sims 3 Steam CD Keys not working

Merry Christmas!

I'd appreciate a bit of help. I just got myself a Mac Airbook and have only just realised that my Steam game of Sims 3 isn't valid with the mac, and so I was told to gather the CD Keys from Steam (which I have done) and download Origin to validate the keys and download them into the Mac. However, It says that the 'code has already been used'.

After scouring the internet for other solutions, I was told to validate it through the Sims 3 website directly, but the same instance of 'the code has already been used' comes up. I'm not sure what else to do, and I've been told that EA Support aren't usually a big help to Steam users

If you can give any advice, it'd be well appreciated.

Thank you!