Hi Alla,
To narrow down the root cause of the issue, I would like to confirm some information below:
1. Do you mean you cannot log into Outlook Web App (OWA) via
https://outlook.office365.com/owa/ ?
2. Please send us the screenshots of the error messages if you have seen. To upload images, please click Use rich formatting and then select the Insert/Edit Media button.
3. How did migrate your Outlook.com account to Office 365?
4. Please remove the license and re-assign the license to see if there is any improvement.
Thanks,
Ran