Oooh ok, I think I figured it out. I had to array the taxonomy stuff into tax_query separate from the other stuff.
'tax_query' => array(
'relation' => 'AND',
array(
'taxonomy' => $TaxName,
'terms' => $Term
),
),
'post__not_in' => array($this_post),
'post_status' => 'publish',
'posts_per_page' => 3,
'order' => 'DESC'
That did it for me.