I managed to solve it and my error was a very basic one.
I just had to call my field with an ID, such as:
$title = get_field('title', $post->ID);
$caption = get_field('caption', $post->ID);
adding $post->ID in order to be able to reference the template part from anywhere, just because I was pulling this info from a post object.
For those seeking the same, these have been enlightening links:
http://www.advancedcustomfields.com/resources/how-to-get-values-from-a-media-attachment/
http://www.advancedcustomfields.com/resources/how-to-get-values-from-another-page/
