My phone is being remotely controlled

If your account usernames and passwords were taken, then it is possible your accounts have been compromised, but that phone is not being remotely controlled. I suggest you change your Apple ID password immediately. If you think your Apple ID has been compromised - Apple Support

Unless you have jailbroken your phone and allowed someone unlimited access to your device and your Apple ID and password, it is not being remotely controlled. What makes you believe that is happening?

If you continue having issues, you would probably be better off contacting Apple Support and maybe getting a Genius Bar appointment if you have an Apple Store close by. They can help you understand things as well, much easier in person than typing back and forth here.