I figured out the solution to this. I just need to add a conditional around the code that displays the image. In the conditional I can access the label by calling $_image->label. Like so:
<?php foreach ($this->getGalleryImages() as $_image): ?>
<?php if ($_image->label == 'somelabel'):
<?php // code to display the images ?>
<?php endif; ?>
<?php endforeach; ?>