It sounds like you redeemed the code successfully but hit "b" and cancelled the download of the online pass\premium file before it could be downloaded to the HDD. Going to your download history and re-downloading your online pass or Premium file to your console should fix this. Since you're on your computer it's easiest to log into the Xbox Live site at http://www.xbox.com/en-US/ and then go to "My Account" and then "Purchase History" and then scroll down until you see your online pass and click "Add to Queue" and then the next time you log into your Xbox your queued items will automatically download to your Xbox.
After you redownload both the online pass and the Premium to your console make sure that you restart BF3 so the game initializes with the Premium file present. When you get to the main title screen you will receive a pop up stating you are now premium and you will have a Premium background. Next you will have to download the DLC expansions covered by Premium (the file just gives you access to download them but doesn't download them for you) via the Premium tab of the BF3 in game store (not via the Xbox Live Marketplace or it will charge you money again)then close BF3. After all 5 expansions completely download (this could take a while since each expansion is about 2 GB) start BF3. At the main menu you will receive a series of pop ups stating that you now have each expansion. Now from the main menu go to multiplayer, open server browser and then open the server browser filter by clicking R3 and check all new maps and game modes or you won't find any games on the new expansions.
