I can't unlock to change my Admin password

I was recently at the Apple Genius Bar because of iCloud issues. The tech surmised that online Apple support had merged my phone iCloud email address account with my MacBook Air email address account (different email addresses and different passwords). She fixed it so that now both are using one email address and one password. The password I am using is the same as my Apple ID. Now I have several issues. A Malware software update prompted for my password and I entered my Admin password, but it would not accept it. Someone suggested that perhaps the version of OS that I am using may not accept an Apple ID password as an Admin password. I attempted to unlock to change my password, but that also will not accept my password. This is very frustrating to me, as I assumed all was fixed. Can someone help and also clarify for me the difference between my Apple ID password, iCloud password and Admin password.

Thank you

Claire