apple id verification code won't work to connect iMessage and FaceTime to MacBook

Ok, so I have a MacBook Pro (2015) running OS X Yosemite version 10.10.5 and an iPhone 5s 16g iOS 10.3.1 (both up to date).

I was watching videos on my laptop, everything was running fine, iMessage and FaceTime were connected, internet connection was working; I go away and leave my laptop for maybe 10-15 minutes; come back and re-enter my password to get back to what I was doing. Come to discover a few pop-up windows that show up a few times regarding iMessage & FaceTime and how they've been logged out and to re-enter my password. So I do this for FaceTime first. It prompts my phone to ask "Allow" or "Don't Allow" user at my location to access; I press Allow and then my phone shows me the Apple ID verification code, I enter this.

Thinking all is good I go to open iMessage to re-connect. But now after getting the code, I try entering it where it tells me to, in the password section after I enter my password. But it just opens a box that keeps telling me I've entered my password incorrectly. I try entering the verification code before my password and after my password; same thing every time. And every time I enter my password it just prompts a new code on my phone. And its driving me crazy and I can't seem to log into my iMessage OR FaceTime on my laptop now.

Anyone had and solved this problem? I can't get it to re-connect for some reason. And yes, I've tried turning both Macbook and iPhone off and on and even turned off iMessage and FaceTime on my phone and restarted it. No luck. I've even changed my apple ID password. Please help. Thanks!