Sign in to iTunes endless loop

I wanted to update my Mac, but when I try to sign in to iTunes, I enter my password and it doesn't accept it. I went ahead and changed the password, in case that was the problem, then signed out of my apple ID on my iPhone, but it still won't accept my password. Even when I click cancel, the box just keeps popping up telling me to sign in to my account. And I can't sign out from iTunes on my Mac, because the first thing it does is ask me to sign in, and the whole cycle starts over again!! Pulling my hair out!!