If I am understanding the question correctly, you should be able to do a query for the media by user id. Something like the follow (untested) code:
//only do this if there is a user logged in
if( is_user_logged_in() ) {
//get the currenly logged in user
$user_ID = get_current_user_id();
$upload_args = array(
'post_type' => 'attachment',
'author' => $user_ID
);
$uploads = new WP_Query( $upload_args );
}else{
//what to do if there is no user logged in.
}
Hope it helps!