Why does my iphone6 SMS page have a big white circle?

Because you shared an ID, you shared your information with others.

Because both your devices have the same appleid in icloud. You can click Settings -I cloud- to turn off the functions of documents and data inside. If there are other data that you don't want to enjoy, you can also turn off the switch separately.

Or if you don't need a device, just log out of your icloud account or log in to another appleid account.

I hope this helps.