Evutis01 If all you redeemed is Ambitions, it should show up on your account under Sims 3 > Manage > Manage add-ons, sometimes with a small delay, and you may need to clear the EA App's cache as well:
https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/
The message about needing to own the base game is standard and doesn't mean the App thinks you don't own the base game. And since a code can only be used once, even on the same account, it's also normal that your code showed as already redeemed the second time you tried to use it.
As an aside, on the Store site, you'd need to click Register a Game to register an expansion or stuff pack. Redeem a Code is for Store worlds and other bonus content.
If you're also trying to redeem a Store world, please see my post just above this one.