Install realvnc on your home box, get a dyndns url forward to it’s IP address and connect via dyndnyaccount.dyndns.com:5800 to your pc at home. That way you can remotely control your home computer from a browser and open websites on your own box that get displayed somewhere else, even if only in 64 colours.
You might change port forwarding in your router to another port if 5800 is blocked in your school so you can access it from 80, which will be open. On the other side it’s not impossible to get hacked that way, so you might also change it to some random wierd port that might be open.