Using short codes in PHP

I am trying to use short codes in a php script that pulls data from another database and outputs to a page on my wordpress site. The code I’m using is:
echo do_shortcode('[wp_colorbox_media url="https://..../trailers/pics/thumbs/$Name" type="image" hyperlink="..../trailers/pics/$Name"]');

Of course, the “….” in the code above has the actual URL for the image. What I get on the page is: Please specify the URL of your media file that you wish to pop up in lightbox

for each image that should be displaying. The $Name variable isn’t being populated instead the exact code above is being output. Any ideas?

https://www.ads-software.com/plugins/wp-colorbox/