I just finished writing a couple pluginsto do this similar thing. I wrote my own plugin to add the extra fields - but it looks like the one you've already used is very similar.
I had a really hard time figuring out how to add the fields for frontend editing as well. But I finally figured it out.
First, you're going to need to copy the com_content form edit.php into a template override (/templates/your_template_name/html/com_content/form/edit.php).
In that file, add the extra fields you have. You'll need the name of the field that you put in the xml file for your plugin you already have. Add them right before/after the fields that are already in the file, that you want your fields to appear before/after. Example:
<!-- CUSTOM begin custom fields -->
<?php echo $this->form->renderField('video_url', 'attribs'); ?>
add all your fields in there - replacing 'video_url' with your own field name. The plugin you already have already saved these fields to the 'attribs' part of the article, so you can leave that there.
The plugin that I used to create the fields for the backend is a really simple one based off of this tutorial https://zunostudios.com/blog/development/203-how-to-add-custom-fields-to-articles-in-joomla
What I'd suggest is to go ahead and create that plugin too. Except in the zfields.php file, change "$app->isAdmin()" to "$app->isSite()" - make sure the xml files have the same names as your other plugin xml files, so they save to the same place, and you're done. The fields will show up on the frontend edit form now.
What I'd really recommend is to get rid of the Aixeena plugin, and just make that easy plugin using the tutorial above - it's super easy. When you make it, duplicate the "if ($app->isAdmin())" section, copy it right below it, and change "isAdmin" to "isSite" - and now you've got the entire thing, all your custom fields, both frontend and backend, all in one place. Now just do the edit.php template override, and you'll have them displayed in both the front and backend. I hope that helps - if you need I can upload more example code.