Curious what you mean by "Webshells". There is such a thing as a web shell, but it's extremely unlikely you're seeing even one, much less one for every site you visit, unless you're specifically trying to. Actual malware wouldn't do that either. So I assume you mean something else but I don't know what. CSS (stylesheets) not loading? Dynamic content not populating HTML templates?
That sounds much more like a hardware issue (misconfigured or dodgy RAM, underperforming power supply, glitchy add-in board, HD/SSD/CPU/chipset on the edge of death) or possibly firmware issue (though I'd hesitate to update firmware on a machine glitching so badly unless the mobo has a built-in rollback feature) than like a software one. This is especially true if reinstalling the OS doesn't fix it.
Assuming it's a hardware issue, that isn't relevant to Security.SE, but you might be able to find help elsewhere for diagnosing and fixing the issue. Regardless, make sure you have everything you care about backed up!
If the motherboard firmware (UEFI, often incorrectly still called BIOS) is actually compromised/malicious, then... well, you can try updating it, but I wouldn't expect that to work. It shouldn't be possible on most systems to load unofficial firmware, actually, but some boards have worse security than others, or maybe you turned off signature checking at some point.
If some other device (HD/SSD?) has bad firmware... that's technically possible but I'd be even more surprised. You can check by swapping the storage to a different machine (or another machine's storage into this one) and seeing how it works then?
