The simplest way is to use the built-in custom fields. If you don’t see them by default, while you’re editing a Post/Page/CPT, choose “Screen Options” at the top right of the screen and check the “Custom Fields” box. Then scroll down through the editor until you see the Custom Fields box. Decide what you want to call your field, something unique with perhaps a prefix – like wpse_second_image – that you’ll remember to use each time in the “name” field. You can then go to the media library, find the image you want, and copy and paste the URL into the “value” field.
Once your images are set, you’ll probably want a fallback image in case you forget to set it or mis-type the field name. Something simple like this will do:
<?php
// make sure the Post object is available
global $post;
// get the "wpse_second_image" custom field for this Post
$second_image = get_post_meta($post->ID, 'wpse_second_image', true);
// if we found an image
if($second_image) {
echo "<img src=\"$second_image\" />";
// if we didn't find an image, use a fallback
} else {
echo "<img src=\"/path/to/fallback/image.jpg\" />";
}
?>
You’ll put this wherever you want the image to appear in your theme. Sounds like header.php in a child theme may be appropriate for your needs.