Do you have $email=$_POST["email"] on that page?
Your sql should be "SELECT email FROM contacts WHERE email = '$email'", or something like that. You only want to know if there's a record with the same email address, so that's why the WHERE clause.
Then if (mysql_fetch_row($result)) is true, meaning there's at least one record pulled, "Your email address already exists!"; You don't need a while statement, one record pulled is too many.
If you didn't set $email, that may explain why the test passes every time. $email and $get_info[email] may both be NULL. (It should be $get_info["email"].)
update: yelvington probably has the better explanation.