How did you manage to install google authenticating app on your phone without logging on to your account? have you tried to sign in with the same account registered on that exchange on your phone and then installing the app to see if it works? 2FA authentication activated on your exchange account is using the email that you have registered your exchange account.
There is an app that would let you to have your phone's screen on your browser while connecting via USB, do you have debugging mode activated on it or not? try airmore to see what happens, if it didn't work, fix your screen.