TheStolenSon,
It’s not having you redownload the game - you only downloaded the free version of the game on your other account. Because Call of Duty is so large, the free version of the game is only about half of the game data. You’re currently downloading the other half of the game data now for the full version of the game.
In this case your best bet is going to be allowing the download to continue. We’re aware of some slow download issues at the moment, so I’m sorry that this is impacting your ability to play your new game as soon as possible.