I think the easiest way to tell if you're using a 32/64bit version of IE is to make a few assumptions and check your process list in the task manager.
Open the Windows Task Manager (Ctrl+Shift+Esc) and find Internet Explorer running on the 'Applications' tab; Right-click it and click on 'Go To Process' which should highlight 'iexplorer.exe' on the 'Process' tab.
It sounds like you're running a 64bit OS so if you're running a 32bit version of IE, a '*32' should show up next to the process. If you don't see the '*32' next to the process, you are running a 64bit version of IE.
1. You can't run 64bit software on a 32bit OS therefore all software on 32bit OS is 32bit.
2. All processes running on a 64bit OS that don't have a '*32' next to it is a 64bit process.
3. All processes with a '*32' next to it is a 32bit process running on a 64bit OS.
Hope this helps!
Law of Logical Argument: Anything is possible if you don't know what you're talking about.