You won't be able to keep the users from seeing the files of others. But you can lock them out of them.
At the folder level change the NTFS permissions. Click Advanced. Assign Creator Owner the rights of Modify/Read & Execute/Write/Modify/List and select Files Only from the drop down.
Remove any default user permissions that contain the groups Everyone or Domain Users.
check the box to replace permissions on all child objects. Click Apply and you should have what you wanted. Your users will still see the files of others but won't be able to open them.
If you mess anything up, you may have to take ownership of the files to be able to change settigns again, so be sure that the Admin account has Full Control on these files before clicking Apply, unless of course the Admin should not have rights to the files.
I hope you find this post helpful. Please let me know if it was.
Regards,
Mark