We'll create fresh WordPress site with Categories Images installed. You have 20 minutes to test the plugin after that site we'll be deleted.
The Categories Images Plugin allow you to add image with category or taxonomy.
Use <?php if (function_exists('z_taxonomy_image_url')) echo z_taxonomy_image_url(); ?>
to get the url and put it in any img tag or simply use <?php if (function_exists('z_taxonomy_image')) z_taxonomy_image(); ?>
in (category or taxonomy) template.
Also from settings menu you can exclude any taxonomies from the plugin to avoid conflicting with another plugins like WooCommerce!