Go daddy is very un reliable for sending emails using a php script. I have had numerous problems in the past with emails not working using Go Daddy's servers. In some cases, I have seen the GoDaddy servers take a long time to send the email message, up to 24 hours.
In the Universal Email settings, there is a setting to include the From address as an extra perameter, make sure thios is selected.
You may aslo need to add the following code to set the mail from address in the php.ini:
<?php ini_set('sendmail_from','firstname.lastname@example.org'); ?>
make sure you have the from and to addresses entered in lower case, not in capitols.
Make sure you are using a Linux based hosting package, many people have had trouble with the email not sending using Windows based hosting with GoDaddy.
In the long run, I have run into more problems using GoDaddy than with other hosts like 1 and 1 or Dreamhost. It would be worth it to switch to different host.