get_posts that match a user-specified value on a page

Using a variable will make your code a little less repetitive:

$case_history_code = get_field( 'case-history-code' );
if ( $case_history_code ) {
    // make the code lowercase
    $case_history_code_lower = strtolower( $case_history_code );

    // use the lowercase inside of `get_posts`
    $myposts = get_posts( 'numberposts=3&offset=0&category_name=" . $case_history_code_lower );
    foreach ($myposts as $post) :
        setup_postdata($post);
        ?>
        <a  href="https://wordpress.stackexchange.com/questions/220489/<?php the_permalink(); ?>">&nbsp;</a> <?php the_excerpt(); ?><br />
        <a href="<?php echo get_permalink(); ?>"> Read More...</a><br />
        <?php
    endforeach;
    wp_reset_query();
}