You currently don't have any active bans at this time. Sounds like you will have to update your game's anticheat (Punkbuster).
Please make sure the game is closed, and proceed to download the updated installers from the link provided below. Download the setup and service installers (PBSetup and PBSVC) and run both of those respectively.
Afterwards you should be all good. If this doesn't resolve your issue, please connect to one of our servers using Battlelog to get a detailed kick message. Make sure the game is closed, EA app is open, and logged into Battlelog. Join one of our servers and you will see a detailed kick message in the red banner at the bottom of your web browser if you are kicked again.
Battlelog is a free social platform that ties into Battlefield 4 and Battlefield 3 and lets you socialize, track stats, plan your next game, and more from your web browser!