We would need some helps regarding our API integration with orders and payments.
We are helping our clients to take the sales call and place orders and payments through the call. I've looked through Shopify's API documents and looks like only a Sales App Channel can have access to the Checkout and Payment API - that means we need a public app.
The thing is we are taking orders through the call so we are not building any interface for end clients. We do have a internal system for our agents to use who take the call but it cannot be accessed externally. This internal system is where we will integrate with the order, checkout and payment API.
This app needs to be reviewed by Shopify before it can be installed. Contact the app developer for more information about this app.
Does anyone knows how could we get a public app approved by Shopify in this case without any public interface? Or if there's any other alternative ways we can use the order, checkout and payment APIs without a public app?
No you at least need a minimal public app so the customer can accept what permissions to give you and who can disconnect you any time they may want to.
The only other way to do it, is by becoming a Shopify Partner and being giving access to manage their ecommerce and install on their behalf. But this is a bit overkill in all the scale scenarios I can think of.