Q: iPhone 6 possibly hacked?

You Apple ID may have been compromised. Try the steps here asap:

If you think your Apple ID has been compromised - Apple Support

Change your Apple ID password and your iPhone Passcode.

First and foremost, get to https://appleid.apple.com and make sure you change your password and security questions there.

Also, make sure your email serving as Apple ID main account is not compromised, so change that email account password as well.

Make a backup of all your information and that should do it.

If they had access to your email they could reset your password, same if you are using that email account with services of the kind of 1Password or Lastpass.

Also, if that's a second hand device, the original owner could still have access to it. Call Apple and make them add it (or do it yourself if you can) to https://supportprofile.apple.com

If your device is not jailbroken, there is no other way they could be using it.

Please contact Apple ID Security asap:

Contact Apple for help with Apple ID account security - Apple Support

Sure but first follow elcpu advice and report to Apple.

Your Apple ID is an email address, either icloud.com so Apple proprietary or whatever other provider you may be using. The first step when you forget a password and don't have two factor authentication in place is to retrieve a link which will be sent to your inbox so you can change when you forgot. If they have access to your email account, they can request a forgotten password link and work from there. That's why you should also change your email password, not only your Apple ID password.

And when the issue is solved, checking this will be worth it to further increase your account security:

Two-factor authentication for Apple ID - Apple Support

Trying to get an explanation here will not resolve your issue. Call Apple ID Security before there is further damage.

Turn Wi-Fi and cellular data OFF.

If this behavior still continues, its an indication that the phone is not controlled remotely (which is unlikely anyway), and check if a "friend" with a warped sense of humor installed a "trick" app.

BTW, is this phone jailbroken?

Your phone has not been 'hacked. That's symptomatic of a failing touch screen. It's a hardware problem, nothing more.

Make an appointment at the genius bar.