Someone Accessing my messages

[MINWATERS]

I keep getting the VZW Free Msg: Your Verizon Messages account was recently accessed from a new browser or device.  Don't recognize this activity?  Please login to My Verizon and change your password.

I've changed my Verizon password & Apple ID multiple times, but someone is still accessing my account--I keep getting verification codes texted to me from sites like Circle, Authy, etc, that I'm not signing up for.  Anyone else having this problem, or now how to solve it?

[SuzyQ]

Does anyone else have access to your Verizon account?  Do you share your apple ID with anyone else on your Verizon account?