I would use Post My Contact Form plugin extension. You can map your form to a custom post or an existing post type, and map individual form fields to custom post fields.
Each form submissions are stored as a post in your dashboard and the author of the submission is set to the logged in user. Therefore when you display your form, you can display a table (above or below) with the previously submitted posts for that user. You’ll need to get all the posts for that author in your page template using a custom query like,
// The Query
$user = wp_get_current_user();
$args = array(
'post_type'=> 'my-form-post' //the custom post type to which you mapped your form.
'post_author' => $user->ID,
);
$the_query = new WP_Query( $args );
// The Loop
if ( $the_query->have_posts() ) {
//build your table here....
echo '<ul>';
while ( $the_query->have_posts() ) {
$the_query->the_post();
echo '<li>' . get_the_title() . '</li>';
}
echo '</ul>';
/* Restore original Post Data */
wp_reset_postdata();
} else {
// no posts found
}