WordPress database error – Error in SQL syntax – I can’t identify any error?

You want the query to look like this:

SELECT email FROM wp_my_users WHERE email="[email protected]"

instead of this:

SELECT email FROM 'wp_my_users' WHERE email="[email protected]"

So try to construct your query with:

 $sql = "SELECT email FROM {$my_table_name} WHERE email = %s";
 $result = $wpdb->get_var( $wpdb->prepare( $sql, $email_address ) );

where you don’t need to escape the table name, since it’s constructed it in a safe way.