PHP Submit form into MySQL table over 2 pages

I'm having trouble with the following code. I need my form to insert information into my MySQL table across 2 pages. I've done some research and with help, I've come up with the following.

First page PHP

<?php
 ob_start();
 session_start();
 require_once 'dbconnect.php';

 if( !isset($_SESSION['client']) ) {
  header("Location: homepage_login.php");
  exit;
 }
 // select loggedin users detail
 $res=mysql_query("SELECT * FROM clients WHERE client_id=".$_SESSION['client']);
 $userRow=mysql_fetch_array($res);


 if( isset($_POST['btn-nxt-page']) ) { 

  $client_student_id = trim($_POST['client_student_id']);
  $ss_name = trim($_POST['ss_name']);

  $client_student_id = strip_tags($client_student_id);
  $ss_name = strip_tags($ss_name);


 if ($_SELF) {
  $query = "";
  $res = mysql_query($query);

  if ($res) {
   $errTyp = "success";
  } else {
   $errTyp = "danger";
  } 
 }

     function redirect($where){      
       header("Location: $where");
    }
    if ($_REQUEST['ss_name'] == 'John') {
    header("Location: http://localhost/homepage_loggedin_book_john.php");
} else if ($_REQUEST['ss_name'] == 'Smith') {
    header("Location: http://localhost/homepage_loggedin_book_smith.php");
} else if ($_REQUEST['ss_name'] == 'Greg') {
    header("Location: http://localhost/homepage_loggedin_book_greg.php");
 } else if ($_REQUEST['ss_name'] == 'Jess') {
    header("Location: http://localhost/homepage_loggedin_book_jess.php");
 }}
?>

First page HTML

<form action"" method="post">

      <div class="form-group">
             <div class="input-group">
             <input type="text" name="client_student_id" class="form-control" placeholder="Enter your Student ID" required />
                </div>
            </div>
            <br>
            <br>

       <label for="ss_name" id="menu">Select a teacher</label>
            <select name="ss_name" id="#menu">
               <option value="John">John</option>
               <option value="Smith">Smith</option>
               <option value="Greg">Greg</option>
               <option value="Jess">Jess</option>
            </select>
            <br>
            <br>

        <div class="form-group">
             <button type="submit" class="btn btn-block btn-primary" name="btn-nxt-page">Next Page</button>
            </div>

         </form>

This all works fine, but the information the user puts in (student ID and the teacher) doesn't go into my database.

This is my second page PHP:

<?php
 ob_start();
 session_start();
 require_once 'dbconnect.php';

 if( !isset($_SESSION['client']) ) {
  header("Location: homepage_login.php");
  exit;
 }
 // select loggedin users detail
 $res=mysql_query("SELECT * FROM clients WHERE client_id=".$_SESSION['client']);
 $userRow=mysql_fetch_array($res);

$_SESSION['client_student_id'] = $_POST['client_student_id'];
$_SESSION['ss_name'] = $_POST['ss_name'];

if( isset($_POST['btn-book']) ) { 

 if ($_SELF) {
  $query = "";
  $res = mysql_query($query);

  if ($res) {
   $errTyp = "success";
  } else {
   $errTyp = "danger";
  } 
 }
}

?>
<?php
$ss_name = $_SESSION['ss_name'];
$client_student_id  = $_SESSION['client_student_id'];
$reason      = $_SESSION['reason'];
$slot_date = $_SESSION['slot_date'] ;
$slot_line    =$_SESSION['slot_line'];
?>
<?php
    $query="INSERT INTO appointments (,
    ss_name,
    client_student_id,
    reason,
    slot_date,
    slot_line,
     )
    VALUES('NULL',
    '".mysql_real_escape_string($ss_name)."',
    '".mysql_real_escape_string($client_student_id)."',
    '".mysql_real_escape_string($reason)."',
    '".mysql_real_escape_string($slot_date)."',
    '".mysql_real_escape_string($slot_line)."','
    )";
    echo $query;
    mysql_query($query) or die ('Error updating database');
    ?>

And my second page HTML:

<form action"" method="post">
    <p>Date: <input type="text" id="datepicker" name="slot_date"></p>

       <br>
       <br>
       Select a line:
       <ol id="selectable" name="slot_line">
  <li class="ui-widget-content">Line 1</li>
  <li class="ui-widget-content">Line 2</li>
  <li class="ui-widget-content">Line 3</li>
  <li class="ui-widget-content">Line 4</li>
  <li class="ui-widget-content">Line 5</li>
  <li class="ui-widget-content">Line 6</li>
  <li class="ui-widget-content">Line 7</li>
</ol>
<br>
<br>

<p>Reason for appointment: <input type="text" name="reason"></p>

        <div class="form-group">
             <button type="submit" class="btn btn-block btn-primary" name="btn-book">Book</button>
                </div>
</form>

I've been advised to put the second page PHP code to put the information into a separate page however I can't connect the pages.

So, my question is:

How do I get the information to insert into my database table (called appointments) across my two form pages?