You can get the required information from the *_IDENTIFIERS static database views.
First, enable PL/Scope and recompile your packages, as per Is there any way to determine if a package has state in Oracle?
The following query returns the public constants and variables.
SELECT ui.object_name,
ui.name,
ui.type
FROM user_identifiers ui
WHERE ui.object_type = 'PACKAGE'
AND ui.usage = 'DECLARATION'
AND ui.type IN ('CONSTANT', 'VARIABLE')
ORDER BY ui.object_name,
ui.name
/