The post box on your Facebook Wall is only visible to your confirmed friends, although it is possible to remove it from their view, as well. Your privacy settings decide who has the ability to post to your Wall on Facebook. To remove the post box from your Wall, you will need to change your Facebook account privacy settings. Once the box has been removed, you are the only person that will have the ability to post to your Wall.
Log in to Facebook using your email address and password. You will be redirected to your profile page.
Click "Account" from the top left corner of your screen, then select "Privacy Settings" from the drop-down menu.
Scroll down to "How you connect" and click "Edit Settings" on the right side of the page.
Find "Who can post to your Wall?" from the list of options listed in the pop-up box. Click the box to the right of that option that says "Friends" and choose "Only Me."
Click "Done" to save the settings.