Dear Mamiy Tchakubuta,
Welcome to Microsoft Community.
I understand that you can't view your messages in New Outlook.
I'd be happy to help you, but I need more detailed information to help you, what domain is your email address?
If you use Microsoft Mail, you can access https://outlook.live.com/mail/0/ to view your emails, and if you can see your emails there correctly, then try adding your mailbox again in New Outlook.
Please let me know if you can't see your email on the web, or if you're having trouble logging in.
For email addresses with other domains, please log in to the email provider's webmail to see if you can view the email properly, and let me know the domain name.
If there are any errors or prompts, you can also take a screenshot of it and send it to the reply, you can use Ctrl + V to paste the screenshot into the edit bar.
Looking forward to hearing from you.
Best Regards,
Jason.YA - MSFT | Microsoft Community Support Specialist