I have a database which contains order information and their tracking numbers and I would like to update the order in Shopify as fulfilled with the tracking number.
Does anybody know of any software that can update the shipment information to Shopify directly from my database?
Or any suggestions/help on how to build that sort of app using API.
I doubt there is any sort of generic adaptor that will interface with your own database sitting on your server and communicate with a Shopify store. You only get this sort of integration if you use a specific drop shipper, fulfillment service, or order processor (like ShipStation) as they have built these integrations already.
With that said you can certainly build an app to do this. The easiest place to start would be to build a Ruby on Rails app that connects to your database and use the Shopify Api gem (https://github.com/Shopify/shopify_api) to communicate with your store.
If this is out of your wheelhouse you can always engage a Shopify Expert to help you out.