Yes. All the USB stick contains is files and folders. Unless you purposely copy the registry area with your browser history in, it couldn't possibly show up.
Imagine I have an empty USB stick and I put squarebear.doc on it to show a friend. That file is all that is on the stick. Nothing else is there.
I think you'd find it very hard to copy the registry (or any other files/folders that contain anything like browsing history) by accident, they are hidden files as default.
If you don't know how to do it, believe me, you haven't copied it. You would need to export your registry after finding the key that holds this information.
If all you copied on are files and folders, that is all that will appear on the stick.
Is everyone answering the question angel21 asked? It seems to me she isn't concerned that she may have picked up files/browsing history onto her USB stick- she wants to know if the record of files she browsed from her USB while using the other person's PC will show up on the browsing history on this other PC.
Angel- were you browsing the net or looking at Word/Excel files from your USB?