Hi Laura,
The same thing happened to me when I got to work this morning, my WP sites were spitting out the same errors.
The first thing I tried worked for me: delete all the empty lines at the end of wp-settings.php, so that there are no spaces or carriage returns after the closing php tag
do_action('wp_loaded');
?><--no spaces/lines after the closing tag
Try that, it worked for me