Unable to log into Apple ID on Mac with fully updated software

I recently changed the email address associated with my Apple ID. I'm now trying to log into my Apple ID on my Mac. Each time I enter my (correct) Apple ID and password in the "Sign In" portion of Device Settings, it just asks again for the login credentials without appearing to have done anything. If I log into my Apple ID on my phone and/or a web browser it shows my Mac as one of my "devices" but it is, in fact, not a device as I've been unable to actually log into my Apple ID. If I "forget" my Mac as a device and then attempt to log in to my Apple ID, I'm presented with two-factor authentication but after typing in the (correct) verification code, it's as if nothing happened and I'm right back to square one. My iphone works just fine with my apple ID.