Kathi,
I was so stiff the first few weeks after my surgery that the slightest head tilt in any direction was horribly painful. I was in a hard collar and my neck felt like stone at times! You're just 1 month out of surgery and going to attemp exercises?...I sure hope you mean stretching exercises!

Anyhow, you're right with the computer position might be aggravating things a bit. Holding your arms up puts a strain on your neck and back muscles, so try to take it easy, and most definitely don't be doing the vaccuuming. Get some rest!
Best wishes,
Kim