Separate User Table in WordPress with Session

I have WordPress website where I setup my own table to store users login credentials. People can register fine but when it comes time to login and create a session it doesn’t seem to work.

This is in my header:

<?php
    // Initialize session
    session_start();
    // Initialize DB
    include("functions/connect.php");
    <span class="login">
          <?php
            if(!empty($_SESSION['LoggedIn']) && !empty($_SESSION['Username']))
            {
          ?>
            <p>Welcome, <?php echo $_SESSION['Username']?></p>
          <?php
            }
            else
            {
          ?>
            <p>Login</p><p>|</p><p>Signup</p>
          <?php } ?>
    </span>

This is on my login page.

<?php
    	if(isset($_POST['name']) && !empty($_POST['name']) AND isset($_POST['password']) && !empty($_POST['password']) AND isset($_POST['name']) && !empty($_POST['name'])){
    				$username = mysql_escape_string($_POST['name']);
    				$password = mysql_escape_string(md5($_POST['password']));

    				$search = mysql_query("SELECT username, password, active FROM wp_thread_users WHERE username='".$username."' AND password='".$password."' AND active='1'") or die(mysql_error());
    				$match  = mysql_num_rows($search);

    				if($match > 0){
    					$msg = 'Login Complete! Thanks';
    					//$email = $row['EmailAddress'];
    			        $_SESSION['Username'] = $username;
    			        //$_SESSION['EmailAddress'] = $email;
    			        $_SESSION['LoggedIn'] = 1;
    				}else{
    					$msg = 'Login Failed!<br /> Please make sure that you enter the correct details and that you have activated your account.';
    				}
    			}

    	    ?>
    	    <!-- stop PHP Code -->

    		<!-- title and description -->
    		<h2>Login Form</h2>
    		<p>Please enter your name and password to login</p>

    		<?php
    			if(isset($msg)){ // Check if $msg is not empty
    				echo '<div class="statusmsg">'.$msg.'</div>'; // Display our message and add a div around it with the class statusmsg
    			} ?>

    		<!-- start sign up form -->
    		<form action="" method="post">
    			<label for="name">Username:</label>
    			<input type="text" name="name" value="" />
    			<label for="password">Password:</label>
    			<input type="password" name="password" value="" />

    			<input type="submit" class="submit_button" value="login" />
    		</form>

My code works on a regular php page without WordPress, but as soon as I login on the WordPress site it redirects me to “wp-login.php” also it
never stores the session. The reason I am using this method as I don’t want users to see the WordPress backend at all as well as be able to add new fields and a checkbox for newsletters and lastly I will be implementing a invitation code feature to users that they can generate 3 codes per user and be able to send them out to friends so they can register as well.

I really would not like to use plugins as they don’t really fit the needs I am looking for unless there is a plugin I am overlooking.

EDIT:

This is in my functions.php 

    add_action('init', 'initEverything');

    function initEverything() {
        if(!session_id()) {
            session_start();
        }
    }

Thanks.