@natamaseda You can use the product codes to install from disc as many times as you want. You can only register the codes with EA one time. It sounds like you already did so at some point, which also means the content should be available in the game library of whatever account you used at the time.
If you don't know what account that might have been, try signing into an EA site, or Origin or the EA App, with any email address you have access to now, and clicking "Forgot your password?" If the address is associated with an EA account, it should receive a password-recovery email. Be sure to check the spam folder as well as the inbox.
If that doesn't help, you can contact EA customer support. Take a photo for the base game and each pack showing the disc, its case, and the product code (clearly readable). You can upload these when you submit a case.
I would strongly recommend using live chat rather than email. If you don't see the option, try this link:
https://help.ea.com/en/help-contact-us/?product=the-sims-3&topic=missing-game&category=manage-my-account&subcategory=find-missing-game
Make sure you're signed into an EA site (this one is fine) before clicking the link and that the location in the lower-right corner of the browser window is set to U.S. or U.K.
