You can check out the Shipment tracking & notify app. Once you fulfill the orders along with the tracking number and "Other" option, Shopify sends a confirmation email to your customer along with the link to the order status page, where they find the "Other tracking number".
If you use the app, when your customer clicks on the tracking number, it will redirect to the app's tracking page, where accurate tracking information will be provided based on which carrier you are using since the app automatically identifies the carrier.
Was your issue solved yet? If not, I found this writing about Shipping carrier https://avada.io/shopify/docs/how-add-calculated-shipping-rate-shopify.html
Hope it could help you!
By the way, this is a list of shipping guidelines for Shopify stores. If you have any problem with shipping, you can find a suitable solution on it.