Apple Accounts can be used on multiple devices, including iPhones and Mac. There are good reasons to use it that way, as iCloud services and Store purchases and subscriptions can then be accessible on both devices. The limit per Apple Account is registering 10 devices of the type {computer or mobile}, of which max 5 can be computers. Be sure to de-register any previous devices that you no longer have.
this [primary] account does not work with my mac
Why not? What happens when you try to use it? Do you get errors? What does that say?
and when trying to create a new account, it is telling me that my account can not be created at this time.
How to create a new Apple Account - Apple Support
Apple Accounts need an email address. An account with an apple domain name (e.g. icloud.com) can be created up to 5 times per Apple device in its lifetime, from Settings. An account with a email address from any other email provider can be created without this limitation, but the email address must be not be in use for any other Apple Account, past or present.
Apple Accounts need full user details as asked, including name, (state), country, DoB, a verified email address (respond to test message!), and a payment method local to the country.