No they're not halogen work lights. Just the $10 clamp lights that you can put a regular light bulb in. I have a 10" one and an 8" one.
I have the camera in portrait orientation with the flash bouncing up with the diffuser on.
The shadow is coming from the flash. When standing behind the camera looking at the subject the flash is off to the left, thus the shadow on the right side of the image.
I don't have a lot of space in the room I used on this shot, but I think your right that moving the background further away will help. I was thinking about using a 75 watt bulb on the clamp light to the right of the camera. Maybe point it a little more towards the background. That might not work though. We'll see what happens next time.