Hi Hhannahh
Greetings!
Thank you for visiting Microsoft Community. We are glad to assist!
Based on your description, I understand you need to switch from your xxx@xx.edu account to your @outlook.com account but received error message "Sign-in is blocked" when logging into the Outlook account.
If you have trouble with signing to your outlook.com account, please firstly follow the same steps in Unblock my Outlook.com account - Microsoft Support. If it doesn't work, to recover your account, please kindly try steps in Help with the Microsoft account recovery form - Microsoft Support or using this Sign In Helper tool from Microsoft.
If the above methods failed to you, please reply back to us, so we can involve dedicate personal account team for further assistance.
Meanwhile, if you can’t access your education account as well, please try the following steps:
If you're an end user//if you are admin but other user has admin rights, you may need to contact your organization's administrator to reset your account's authentication method under "Manage MFA authentication methods."
For more information, see this document: Manage authentication methods for Microsoft Entra multi-factor authentication - Microsoft Entra ID | Learn from Microsoft
If you are the admin only, it is suggested to contact business phone support, please check Find Microsoft 365 for business support phone numbers by country or region - Microsoft 365 admin | Microsoft Learn or Global Customer Service phone numbers - Microsoft Support.
During the phone call, press "1" as a business email user and press "1" again for technical support. You may be asked for certain information for verification, such as account or subscription information, organization information, and phone number.
Please note that you must call the hotline Monday through Friday (9 a.m. to 5 p.m., Monday through Friday),sincerely apologize, and thank you again.
Your patience and cooperation will be greatly appreciated. I hope all the best!
Sincerely,
Connery You
