I think this may help....
If your Tickets computer is in your office (and I think it is), then......
Determine your public IP address. If you don't know it you can go to
www.whatsmyip.org from the computer hosting Tickets.
Give that address to your DNS provider for your subdomain. They will add your IP address to your DNS for your subdomain. It will take up to 24 hours to become effective.
Then, determine the IP address of the computer hosting Tickets.....it will probably be in the range 192.168.x.x
And, get the port number that Apache is using on that computer (probably 80), then.....
Access the router in your network that the Tickets computer is on, and install a port forwarding rule for the port Apache is using, to the computer that Tickets is on.
Now, you just created a web server on the internet.
Mark