It looks like you've downloaded something dodgy off of workshop.
Get all essential files into a USB drive and then take it out (NOT any games). Unsubscribe from all addons and delete them all from your addons folder to be sure. Then delete Garry's mod itself and make sure it's all gone.
Hold down shift and press restart in the start menu. Computer will boot into advanced setup. Do a refresh.
This should give you a chance of having the freshest computer possible to install it on without losing all your files. If it works, I'd install malware detection software and probably the free version of avast. It's the setup I run.
If it doesn't work, there's always the full reset in the cards, which is why you grabbed that USB. It'll be a pain to reinstall everything but at least it'll give you a better chance if the refresh doesn't work.