Hi,
Which version of Outlook are you using?
How did you configure your Hotmail account in Outlook? Via IMAP, POP3 or Exchange ActiveSync?
Please try starting Outlook with /cleanviews switch to check if your emails are hidden or filtered by custom views. To do this, press Windows key + R to open the Run command, type outlook /cleanviews and press Enter.
Please also make sure you have set up your email account correctly. Please have a look at the following KB articles to see the correct steps:
For Outlook 2010 and earlier versions:
https://support.microsoft.com/en-us/kb/2735989
For Outlook 2013:
https://blogs.office.com/2012/11/15/put-the-power-of-outlook-2013-behind-your-outlook-com-email/
If above doesn't work, please also try creating a new mail profile in Control Panel and reconfigure your email account in the new profile to see the result.
Hope it helps.
Regards,
Steve Fan
TechNet Community Support