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  1. UPDATE

    I did not test this method, but it is not very old. It adds custom meta information to the caption section of the image, which can then be styled as needed. Again, I did not try the method, and I am not a coder, but from reading through the tutorial, it sounds like it fits your needs.

    Add Custom Meta Fields to Media Attachments in WordPress

    Original Answer

    I think this article from wpbeginner might be exactly what you need. I have used this exact method before.

    How to Add Additional Fields to the WordPress Media Uploader