Worried I've lost my website

Could be a brief failure at your web host, see if it comes good.
Otherwise contact your hosting support.

Don’t you have FTP access or a control panel to check that your files are still there?

At the very least, you should have an indication of the disk space you’re using. If it’s down to zero, then, there’s a real problem.

If you are using a ‘cheap’ web hosting service you will have this problem every so often. Come back the next day and see if your site is up. If it happens often then I would suggest you move to a more reliable web hosting service.