My code origin just gave me said that it's used

When you purchase The Sims 3 or any of its Expansions or Stuff Packs through Origin, you no longer need to manually register your product through The Sims 3’s website. Just make sure that your Origin account details match the details of your Sims 3 account, and Origin will register your products for you.

If you already have an Origin account and bought The Sims 3 or any of its Expansions or Stuff Packs through Origin, you do not need to create an account on the Sims 3 website. Just log in with your Origin account and you should be able to see your products on your "My Page" website.

Read more about how to register your game here:

http://answers.ea.com/t5/The-Sims-3/Information-How-to-Register-The-Sims-3/m-p/387162

I can see the game on your account. Just log into the Origin client with your account and you should be able to download the expansion.