When you insert the USB stick in your PC the malware will also install its self on the PC? Does the same thing happen when you try to delete it from the USB drive?
Try Hitman Pro and Zemana Antimalware Free to see if they can get the malware.
Can you check Task Scheduler for suspicious entries? You can use Task Scheduler's interface, Sysinternals Autoruns or Comodo Autoruns for that purpose.
To get rid of the malware on the USB stick you could format it. If it persists on the PC then that's a next problem.