Based upon the description it sounds like you need to show the details of the selected tracking number. Tableau provides a dashboard action call URL action. If the URL for the 'tracking info' has a fixed format, then you can use URL actions. You just need to pass the tracking number as a parameter to the URL action.
Go through this link. http://onlinehelp.tableau.com/current/pro/desktop/en-us/actions_url.html
Also watch this video
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Sujay is correct, this is most likely your best (easiest) option. You won't be able to display it in a tooltip though, you'll have to use the webpage option.
If you really want it in the tooltip, you could potentially create a Web Data Connector to pull from the API and connect to that in Tableau, then join your two sources together.