MacBook allows me to login to admin, but won't allow me to unlock system preferences or other admin controls?

I technically have two accounts on my 2013 MacBook Pro. One is my admin that I have always used and the other is just the standard "guest" login option.

I have my password for my admin account and I can log in to the account and use my computer as normal. However, if I ever try to unlock settings, download from unknown source, or install any software, my password and username does not work.

EXAMPLE OF ISSUE: I log into my user called "bob" that has a password that we will call "xxxx". I can login to user "bob". When I go to settings and click the unlock/lock button to change anything at all it just shakes as if my credentials were wrong. SO, I went ahead and changed the password to my account just to see if it was a small bug. Now my new password I know is "yyyy" and it works to login to the user. Still has the same issue when trying to change settings though.

This is my only admin account and I can't create another admin unless I successful pass the credentials. (which I know are correct because I can log in to them)

MY THOUGHT SOLUTION:

I was thinking of backing my entire MacBook onto my 1tb external hard drive. From there I was hoping there is a way to reset my computer and create a new admin account. How can I go about doing this?

Thank you!