You are now pointing your records to local ip address.
Keep the MX records at GoDaddy, and point them to the external ip address of your server.
Does the webform send a mail straight to email@example.com
then open up the mail log (i think it's /var/log/maillog on fedora) and tail it
tail -f /var/log/maillog
Then press send on the webform and see if you get new entries in your logfile.
(Note: don't forget about dns cache, since you're editing dns records)