Re: Game BF4 bought but was not downloaded to my PC

As I can see your Battlelog profile you have Battlefield 4 and Battlefield 3, both profiles have 0 Lvl. Could you please make sure you login in to the correct account? Also, if you have any Filters in your Origin Library, try to remove them.  Try to clear Origin cache https://help.ea.com/en-us/help/origin/origin/origin-my-games-list-is-blank/ then reboot your PC.

If the game is still missing in your Library, contact EA support for assistance:  How to contact EA support