Hmm. You can only send a private message ( known in twitter parlance as a direct message ) to a follower.
If you sent a message as described above, it will go to whoever has the twitter address @natalie which may or may not be your cousin. Additionally, that message will appear on your own timeline, so any followers you had/have would also see it. Think of twitter like a group meeting of followers; All can hear your messages, unless you expressly make them private - but you can only do that by sending a direct message to a follower.
The # or "trending" tag means that anyone following a particular trend that you have addressed with your hashtag will be able to see your message. Thats kind of like taking a megaphone and shouting out your message to the whole world...
https://sites.google.com/a/alaska.edu/iteach/resources/twitter
Not sure if any of that has been of any help whatsoever! :)