Using the Post/Redirect/Get pattern from Keverw answer is a good idea. However, you are not able to stay on your page (and I think this was what you were asking for?) In addition, it may sometimes fail:
If a web user refreshes before the initial submission has completed because of server lag, resulting in a duplicate HTTP POST request in certain user agents.
Another option would be to store in a session if text should be written to your SQL database like this:
if($_SERVER['REQUEST_METHOD'] != 'POST')
{
$_SESSION['writeSQL'] = true;
}
else
{
if(isset($_SESSION['writeSQL']) && $_SESSION['writeSQL'])
{
$_SESSION['writeSQL'] = false;
/* save $_POST values into SQL */
}
}