What hook do I use to add a field to a content type after it was programmatically created?
Try the hook_update_n function
https://api.drupal.org/api/drupal/modules%21system%21system.api.php/function/hook_update_N/7

You would define a hook_update_n function in your install file in which you place the functionality to add your field to your content type. 
See for example:
http://cgit.drupalcode.org/entity/tree/entity.install#n35

After added this functionality run http://example.com/update.php

A second option would be to use the features module to export your content type to a feature and when you are making changes in the UI to that content type (like adding a field for example) you can export the content type again to the feature and deploy that feature to your other (live) environment and revert the feature (which will bring the new code (the newly added field) into the database.