alternate left – right content inside the loop

You should be able to get the current index in loop from the global $wp_query object. With the help of modulo you can then set an alternating css class for a post.

global $wp_query;
while ( have_posts() ) {
  the_post(); 
  $alignment = ( ($wp_query->current_post + 1) % 2 === 0 ) ? 'even align-right': 'odd align-left';

  // post html markup with class="<?php echo $alignment; ?>"
}