You didn't understand the difference between a LAN (Local Area Network) and the public Internet yet. You most probably got an IP address from the private range (192.168.xx.xx or 10.xx.xx.xx) on your Arduino. You can access it with that address from inside the LAN but not from the Internet (these IPs are not routed).
You may be able to configure such an access on your home router but I doubt that your school will do that for you on their routers. Do you really need access over the Internet? Isn't it enough to access it from your mobile device while you're connected to the WiFi network?