It's possible that the ports/hosts used by QuickTime and Software Update are being blocked, so you won't be able to get updates to, say, the security updates for your OS. If this is your school doing so, oi.
You can get the updates from the Apple website: look under the "Support" tab and you'll be able to download and install the updates "manually". meanwhile, contact your school's IT support folks and ask them if they know what's going on. It may be that they are using some form of "proxy" software that is woefully misconfigured.