What has happened here is that you have essentially two accounts: One is your consumer MSA, and the other is an account in the school's Azure AD instance that uses federated sign-in with an external account (your MSA). Except, the real mess comes from the fact that there's one login page for both, and sites such as the Azure portal that support both identities and can't really tell which one you expect to assume. Plus, the Azure portal lets you switch between Directories at any time.
You can:
* Sign out completely (login.microsoftonline.com/logout.srf) and sign back in. The reason the sign-in page asks for your sign-in email first is because then it uses that to decide which directory (MSA or someone's AAD) to sign you into
* Change directories - (in fact I'd recommend creating your own Directory instead of using the one that was automatically created for you from your MSA name)