But if I wanna make another account, wouldn't I need to use one of my invitation codes from this account?
Yeah, that's the idea. When you click on 'use' on the invite page it takes you to the account creation page. When you request the email to manually validate the account it will not have your username in the email but when you click on the link and let the page load it will have the username and it will say that it's been validated.

When you create via one of your invite codes all it does is logs you out of your current account and into the one you just created.

Or.. did that not really answer your question?