Yes your school certainly can track your internet history and see what you're downloading or what websites you're visiting.
Schools also block certain websites from being browsed through their internet connection too because the schools do not want you visiting certain websites or downloading certain files.
Your internet history is always being tracked by the schools and they can look at your browsing history on the schools computers when you use them.
So be careful what you're browsing on the schools computers and on the schools internet.
Especially with the problems of the school shootings that happen now the internet history is being tracked more and more at schools.
You could use an online web proxy to get past some of the schools internet filters that are blocking certain websites but I would advise against it as it might get you into trouble with the school.