You shouldn't need to use the product code for the second time. The game becomes linked to the EA Account you were logged in with when you redeemed the code originally.
If the game is not showing in Origin client when you log in, then the most common cause for this is that you are logging in with the wrong account. Could you please try logging in to Origin client with different email addresses you may have to see if the game show in Origin client under a different account?
PS! If you can see the base game in Origin, but not the expansions then right click the base games tile and select 'View Game Details'.
Let us know how you get on!
