This is probably better done by your mail client than your mail transfer agent (MTA), so leave your sendmail configuration alone (it's a bear to change anyway :-). Most mail clients give you the option of specifying the sender address, which is what will appear on the From: header line in outgoing messages (and also the Reply-To: line). I use Emacs as my mailer, so I can't tell you how to do that in Pine, but look for a Sender Address option.
OTOH, you might mean that you want the address in the message envelope to be
myusername@something.else. The envelope is the addresses your MTA use, which can be different from those in the header. Check out sendmail's virtusertable and local-host-names files, both of which should be in /etc/mail. But if you start changing this stuff and your system thinks it's in the domain "localdomain", it
may just cause sendmail to stop working.
I'd go for the mail client configuration, because it's the easiest, and most likely what you need.