This is the solution that I came up with...
<form method="post" action="<?php echo $_SERVER['PHP_SELF']; ?>">
<select name="select_month">
<?php
if (isset($_POST['select_month'])) {
if($_POST["select_month"] == "January"){
echo '<option value="January" selected="selected">January</option><option value="February">February</option>';
}
elseif($_POST["select_month"] == "February"){
echo '<option value="January">January</option><option value="February" selected="selected">February</option>';
}
}
else{
echo '<option value="January">January</option><option value="February">February</option>';
}
?>
</select>
<input name="submit_button" type="submit" value="Search Month">
</form>