Hey Emmy,
Thanks for reaching out.
Sidebars are generated by your theme, so their location is controlled not by any plugins, but by the theme itself; and so upgrading to Events Calendar Pro would not solve that problem right away.
However, yes, as you mention Events Calendar Pro does have a number of shortcodes. And so, for example, you could make a “page” in your wp-admin with a page template that uses the desired sidebar, and then you could add Events Calendar Pro shortcodes to this page. The generated Shortcode output would be there alongside the desired shortcode.
I hope this information helps!
George