Why does my cell phone keep getting an error message about my password being wrong or account being changed?
First try what Izzy suggested in his comment. If that doesnt help then..

Log out of all Google apps, then...


sign in through appropriate app or.. 
try to sign in through your browser


If neither will work then remove your Google account from your device and re-add your account. Remember to back up your device prior to doing this, otherwise your contacts, messages, and few other things will be deleted. PlayStore and everything else will be fine. 

You might have a connection error after adding your account while validating your info, if so go into your YouTube app and login that way. 

That is how I fixed the problem on my device. I was able to sign right in.