SOLUTION FOUND!
I used this after each while:
<?php wp_reset_query(); // Restore global post data stomped by the_post(). ?>
So the end product looks like this:
// Display ACF content for category a
<?php the_field('category_title_a'); ?
<?php the_field('category_content_a'); ?>
// Display posts from category a
<?php $my_query = new WP_Query( 'category_name=cat-name' );
while ( $my_query->have_posts() ) : $my_query->the_post(); ?>
//extra stuff here
<?php endwhile; ?>
<?php wp_reset_query(); // Restore global post data stomped by the_post(). ?>
