How do I embed something in a sidebar that doesn't have a widget option?

Try putting it in your theme’s sidebar.php

Do I need to create a child sidebar.php first?

I’m using twentyeleven theme and I have already created a child for it
with child header.php and child style.css

yes copy sidebar.php into your child theme and edit it there.

I just need to copy EVERYTHING from parent sidebar.php into child sidebar.php?

Yes copy everything. WordPress is going to use your child theme’s sidebar.php