Hi Tess,
Thank you for the screenshot, is the bottom user on that picture your new account?
if it is, then it is not an administrator account, just a standard account.
You need to log back into the old account, open netplwiz, select the new account and click Properties.
Then on the User Group tab, set that new account as a member of the Administrators Group
Important, do not change the old account there.
Then log back into your new account and in netplwiz you will be able to remove the old account