Is this a script just anyone can fill out? If so you need to add some input checking into the script as it is a bit exploitable the way it is written.
What if someone entered:
one@email.com;two@email.com;three@email.com;four@email.com
etc. and entered an nice long spam email message in the place of their name?
That is only way way to exploit the script.
Second question. What is the switch statement for? It doesn't appear to have a purpose.
Third: Do you have the settings in your php.ini pointing to qmails sendmail interface thing? Can't remember what you would call it at the moment. It should be at like /usr/bin/sendmail
-Michael