If you only bought Battlefield 3 Premium without the basic/standard Battlefield 3 then the game will not appear, you will need to buy the basic game also, then your premium content will also bind to that profile and you will see the game in Origin.
Like many people who don`t read all the description before buying a game you probably made that mistake of Buying only Premium without Battlefield 3. Here read this article: https://help.ea.com/article/what-is-the-difference-between-battlefield-3-premium-and-battlefield-3-premium-edition
Contact EA chat support, maybe they can give you a refund, in order for you to buy the Premium Edition which contains Premium and Battlefield 3.
Regards
theDokt0r