Hello Brody Strock,
Thank you for posting your query in the Microsoft Q&A Community.
I understand that you have created a new Azure tenant with your work email. Since your Organization already exists in Azure, a personal account will be created for you after the process. Hence, your account is a dual account.
Let's start with your work account access, you either force the authentication to this account by accessing your tenant using the URL (portal.azure.com/tenant-id-of-your-organization) or via Incognito. Once you try accessing your account via incognito, you will be presented with the same screen as shown in the screenshot below. Select the work or school account to access your work portal.
For the personal account created, since you won't be able to create a new Azure account using the card, I would advise you just rename it. This will allow you to change the email associated with the account.
Let me know if further assistance is needed.
Babafemi