you don't need to reregister the game if you register on the sims 3 site they register in origin for you or if you register in origin first then they auto register for you on your the sims 3 account
the sims 3 account and origin use the same email and password if you used two different ones then contact CS to assist with merging the accounts
for the expansion pack not showing into log out and log back in to your origin this gets games to refresh/reload account then check the my games tab and download your expansion pack if the other item is a DLC content item you download that from your the sims3 account-my store account-purchase history download and then install the item/s
