A shortcut IS NEVER a virus. Virus want to be stealthy and go to great length to not advertise themselves.
To remove an unwanted shortcut, the best is to uninstall the associated application.
You often have foistwares pushed alongside with MANY installers. Even some payd for applications come loaded with that kind of junk.
ALWAYS sellect "Custom", "Personalised" or "Expert" install and ALWAYS refuse any and all so called "recomended" or otherwize proposed extras. None of those are ever needed and will ONLY clutter up your computer.
You can go to ninite.com to get custom to you, sanitised installer that will automaticaly download and install several free applications while blocking foistwares and pesty side installs. It will automaticaly sellect your language and 32 or 64 bits version according to the capabilities of your system.
It's also a gteat automatic updater: Just run it again and it will check for updates and install those available.
Uninstall those applications that you don't need, want or installed by accident.
If an application refuse to uninstall, make sure it's not running, delete it's folder, empty the recicle bin, install Ccleaner. Use it's registry cleaner to remove leftover registry entries.
Get some reputable antivirus. Some propositions: AVG, Avast, Avira, Malewarebyte, as well as the one from Microsoft. (don't remember it's name) They are all available for totaly FREE.
Install ONE, have it update itself and run a full scan.
Set your antivirus to update it's viral database dayly and to update itself.
Note that the free version Malewarebite is not made to run in the background. It's a very good secondary antivirus to be run manualy.
Install Spybot, have it update itself, run the immunisation and do a full scan.
Be sure that Windows automatic updates is set to download and install all updates as they become available.
Make sure that ALL applications that have some form of automated updating are set to update themselves.
NEVER EVER click any attachment or link from any unexpected e-mails from peoples you don't know, and be sure that those from known peoples are realy sent by them.