Hello Ga1000,
Thank you for reaching out in Apple Support Communities. I understand you're unable to sign in with your Apple ID account in iTunes on your Mac.
iTunes is a great option to backup and update the software on your iPhone. I can help point you in the right direction.
To ensure you're able to successfully sign in with your Apple ID account, I recommend using a web browser and to sign in through the Apple ID account page at: Apple ID account page
If you're able to sign in successfully without an issue, the next step is to restart your Mac in safe mode. Then, open iTunes and see if you can sign in with your Apple ID. Here's a helpful article on how to restart your Mac in safe mode: How to use safe mode on your Mac
Please let me know, if that helps.
Kind regards.