Your game should be linked to an Origin account. You use this to log in and all the game's data is stored to this account. However, you don't need one to play the game. The problem with this is that you can't get friends on the game and you can lose all your data if something goes wrong.
If you have an Origin account, make sure you're logged in with the correct details. If you don't have one, you will have to contact EA help.