Hey Elizabeth,
I'm Alex, your friendly neighbourhood Guru at Shopify.
As of the now, outside of moderating the comments and rejecting those which you disallow for publishing, there isn't an app for that. Something I can suggest however is maybe integrating a third party blogging controller like Disqus which will give you a bit more control over that:
https://ecommerce.shopify.com/c/shopify-apps/t/is-there-an-app-to-block-spam-on-blog-posts-301333
I hope that helps, and I want you to know that we hear you on that one.
All the best.