If both of your "services" actually
use the HTTPS protocol (are accessible with a web browser), then there's almost certainly a way to make them available as
https://your.ip.address.here/service1/ and
https://your.ip.address.here/service2, even if they are served by two different processes. If one of the services (your post doesn't make it very clear what one of them is) uses some other (than HTTPS) protocol and only makes use of por 443 because it's open, then this parobably won't work.
If you can install software on the computer you will be using behind the school firewall, then you could probably use the open port 443 to set up a VPN (e.g.
OpenVPN), which would be capable of fully bypassing all school firewall restrictions by redirecting your network traffic through your home computer.
