Checking on your Checkout page, I can see that only Free Shipping is the only available shipping method as seen below:
To better picture what you are referring to here, can you please share with us a clear screenshot of the following settings below so that we could check this further?
General Settings
Shipping Settings
If you don’t already have a screenshot service installed, you can try https://snipboard.io or http://skitch.com/. You can share the direct link to the image as a response to this topic.
Additionally, I’d like to understand your site properly, please share your System Status Report that you can find via WooCommerce > Status. Select Get system report and then Copy for support. Once you’ve done that, you can paste it into your reply here.
If you could also provide the fatal error logs (if any) under WooCommerce > Status > Logs.