Frontend form input into a shortcode

My target
Frontend input (form of 1 field) for a page or custom post type. A visitor will enter data in the field and click SUBMIT. Then the data will be inserted into a shortcode of a plugin. Only after that, the plugin with the updated shortcode, will run and display in the front end the results.
As an example – the visitor enters a YouTube Video ID in the frontend https://youtu.be/VYuwwXG5i20 and then he clicks SUBMIT. This will have the page in the backend with [embedyt] https://www.youtube.com/embed?listType=playlist&list=UUkYAlrLUqmg5AvQbg7qNHLw&layout=gallery%5B/embedyt%5D which will then used by the plugin https://www.embedplus.com/ ) to create a video gallery of all videos of a channel.

This is just an example. The problem is how to run the plugin AFTER the front end data gets into the shortcode.

Anyone can help?
Thanks!