Copy the file header.php from your parent theme into your child theme.
In your functions.php register a new widget, (use the parent theme as a template). call it like "sidebar-hdr"
Edit the child theme header.php, after the div with id="logo", add a block like this:
<div id="hdr-sidebar" class="hdr-sidebar widget-area" role="complementary">
<?php dynamic_sidebar( 'sidebar-hdr' ); ?>
</div><!-- #hdr-sidebar -->
Then in the Dashboard > Appearance > Widgets, add a text widget to the hdr widget area, add your text here.
Add custom css to style the new text.