I know there's lots of dropshipping Apps that work with pre-determined suppliers and wholesalers . However my suppliers are not on any preordanied/ predetermined list.
Is there any other App on Shopify that will integrate into my shop and that I can use to manage my inventory and alert suppliers of when and where to ship goods to as they are paid for on Shopify?
For the inventory component, you can use an app called Stock Sync which you can find in our app store here: https://apps.shopify.com/cloudcoder-shopify
For notifying your dropshipper of orders, you can set this up under Settings > Shipping > Fulfillment and Dropshipping. Here you can add the email of your dropshipper to add them as a fulfillment provider.
On any of your products in the admin, you can then select this dropshipper under Fulfillment service in the Shipping section of the product.
Check out www.channelape.com, what your looking for is a custom integration to your supplier. channelape can do that for you and may already have the integration built. Check them out, they may have exactly what your looking for.