I would be careful about adding too much text as "alt" text. Some screen readers might cut off after a certain number of characters or - in the case of an image not loading properly - the user might only be able to see the small amount of text that shows up in the space the image should occupy. I think the idea of adding text in a caption is good, or you could add a "long description", depending on how you are sharing this image (social media, in a document, on a website). The
$1 at the University of Washington has additional information about alt text.