Thank you for reaching out with your question. Within Shopify's shipping settings it is not possible to set rates on a provincial basis for Sri Lanka, but there are some apps that may help you achieve greater flexibility when it comes to setting your shipping rates.
The apps in question are Better Shipping and Advanced Shipping Rules. Both apps offer a variety of different features when it comes to shipping settings and rates, and both should allow for more region-specific shipping zones to be set up. I would recommend taking a look at both apps and potentially emailing their developers to confirm that the apps will work for Sri Lankan shipping zones before you opt to use them.
I hope this helps but please let me know if you have any further questions!
Victor | Shopify Social Care