You are most of the way there, you simply have to echo it into the include:
<a href="https://wordpress.stackexchange.com/questions/276748/<?php echo $url;?>/image.png"><img src="https://wordpress.stackexchange.com/questions/276748/<?php echo $url;?>/image.png"></a>
If you are already echoing this whole line, then you simply concatenate the variable:
echo '<a href="'.$url.'/image.png"><img src="'.$url.'/image.png"></a>'
Do some reading on PHP “concatenation” 🙂