Okay, first of all I would not advise trying to circumvent school/work firewall rules.
If they are running a regular off the shelf firewalls then I think your only option is to use something like OpenVPN via port 443.
Set up an OpenVPN server on your ASUS router, set it to listen on port 443 and allow it in your routers Firewall. Once configured export the certificate and put it on OneDrive, USB etc.
At school on your laptop, install the OpenVPN client and provide it the certificate you exported above.
Obviously not knowing your school setup I don't know if their FW is clever enough to sniff out the OpenVPN traffic and block it.
I would have thought most firewalls would block common VPN and screen sharing software such as Teamviewer etc.