I'd assume the route for your home connection is the same for the school. (Or the route for your school is also blocked)
Call your ISP and ask them for a whole new route.
{e.g: your current IP is 1.2.x.x
a new IP with a new route would look like 5.6.x.x}
Depending on your ISP and country, restarting the router might "sometimes" also change the route, but if the route or IP is static, you need to call your ISP.