As for allowing users only to edit and upload their own images, well, WordPress does have basic Access Control Levels. There are also plugins that can refine control. But as you said it is more for post, cpt and or page access.

You do mention that you want users only to upload images with descriptions. Well did you check out https://code.tutsplus.com/articles/allow-users-to-submit-images-to-your-wordpress-site–wp-22601 ? That would allow user to use the frontend to upload images with captions into certain categories. This may not be quite what you need, but gets you going.

You could build upon it or get a developer to work things out. Things that would need to be added is (automatic) loading of image data, registration and creation of user image gallery, sidebar widget. So perhaps this plugin’s functionality could be added to a new plugin with the additional functionality. Perhaps one without the need for NGG altogether.

NB Did you ask the author of gallery plugins like NGG about your needs? That could not hurt either..