yes, U can run a scan with Malwarebytes (just google it)
Does this happen every day or after a certain period of time?
There is the Desktop Cleanup wizzard, (or maybe U have a cleanup program that deletes unused shortcuts on desktop every X days, like Tune up has. What cleaning utility do U use?) that moves your desktop icons (U can look that on Right click desktop>properties>desktop> Customize...bla,bla,bla..uncheck the option or uncheck it in your cleanup program.
U can check if the shortcuts are on a separate folder on desktop, or if they really are in desktop folder, by going to C:\Documents and settings\Username\Desktop
Or see if this happens in another user.