Track down what is putting icons on my desktop
Seems like someone had the exact same issue but posted it on the Android Forums, not here. :(

Things to try:


Install one or several of Airpush Detector, Avast! Mobile Security, AVG antivirus, or/and Addons detector.
Install CM Security to prevent things from slipping by unnoticed again.
Start Uninstalling apps one by one starting with the most recent to see which one is the problem, and then don't reinstall that one.  


I hope you can get your phone back to normal soon!