Search Box in Header

There is a couple of ways to do it.

First check your Theme
Sidebars and widget areas
and se if you have anything related to search that you can uncheck

Next way is in the files of the child theme.
In header.php look for:

<?php
// Has the text been hidden?
if ( 'blank' == get_header_textcolor() ) :
	?>
	<div class="only-search<?php if ( ! empty( $header_image ) ) : ?> with-image<?php endif; ?>">
	<?php get_search_form(); ?>
	</div>
	<?php
else :
	?>
	<?php get_search_form(); ?>
<?php endif; ?>

Highligt and delete that.

Or by css

/* Search Form */
#branding #searchform {
	display: none;