My Mac is not letting me sign in to my hotmail.com account. It just keeps buffering.

Are you using your Mac's Mail app, or are you using a "Hotmail" web mail page?

For Mail, please read Troubleshoot email problems in Mail on Mac - Apple Support.

If I'm not mistaken, the email service once known as "Hotmail" is now either Microsoft Outlook or some other Microsoft service. I don't use their products, so you should ask them: Contact a third-party vendor - Apple Support

Try signing in here: https://account.microsoft.com/account

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply        Pastebin

Etrecheck – System Information