Get link picker custom field to show only if field exists

You’re testing if assigning a value to $mylink was successful in the if statement rather than testing if it’s empty.

Try something like:

<?php 
    $article_link = get_field('article_link');
    if( $article_link['url'] ): ?>
    <a href="https://wordpress.stackexchange.com/questions/246505/<?php echo $article_link["url']; ?>"><?php echo $article_link['title']; ?></a>
<?php endif; ?> 

See Example 1 in the ACF docs.