I'm still not sure about your claim that private information consists _only_ of "information I don't want anyone else to have."
You can share information with another trusted party and still have an expectation of privacy (such that the government needs a warrant to compel access to that information). Conversely, you can have information that you don't share with another living soul, and the government can also compel access to that information - e.g. a warrant to search your private belongings. The standard for how the government can access your information doesn't automatically change depending on whether you've shared it with 0 or > 0 people.
You can share information with another trusted party and still have an expectation of privacy (such that the government needs a warrant to compel access to that information). Conversely, you can have information that you don't share with another living soul, and the government can also compel access to that information - e.g. a warrant to search your private belongings. The standard for how the government can access your information doesn't automatically change depending on whether you've shared it with 0 or > 0 people.