This might be easier to do than I thought…the description is generated in the image title meta…do you have any quick ways to echo that up your sleeve? I will play around with some options and post solutions here.
I think I’ve got it!
Added this line to wp-instagram-widget.php
echo '<li>'. esc_attr( $item['description'] ).'</li>';
I placed it just above:
echo '<li><a href="'. esc_url( $item['link'] ) .'" target="'. esc_attr( $target ) .'"><img src="'. esc_url($item[$size]['url']) .'" alt="'. esc_attr( $item['description'] ) .'" title="'. esc_attr( $item['description'] ).'"/></a></li>';
Glad you found a solution.
Remember that any future updates to the plugin will overwrite your changes. With that in mind there is a potential CSS solution that you could add to your theme. I have not tested the following but something along the lines of:
.instagram-pics img:after {
content:" (" attr(alt) ")";
}
added to your themes stylesheet might do the trick. This will allow you to update the widget in future without worry.