You can't turn them off, but you can clear the suggested searches on Instagram for your iPhone. Here's how to do it, and clear your search history.
You can easily clear your suggested searches on the Instagram app on your Android device in a few steps.
When it comes to my digital life, I've got nothing to hide. But then again, there's stuff I don't feel like broadcasting either. And what I've been searching for on the web is one of those things I'd ...