Hi Katherine,
Sounds like you need to get your IT person to change the way your mail client works. Generally there are 3 options:
1) Copy new emails from the mail server onto your computer (uses a protocol called POP3).
2) Move new emails from the mail server to your computer (also uses a protocol called POP3).
3) Attempt to keep the mail client on your computer and the mail server (i.e. Comcast) in sync (uses a protocol called IMAP).
It sounds like your system was set up to use (1), so eventually your email account with Comcast would fill up.