Without seeing the flickering it is hard to figure out what could be causing the problem. If it is still happening after a complete tower and monitor swap you are probably getting hit with EMI. I’ve seen cubicle desks that have the under cabinet lights above the monitor cause problems like this when the bulb or starter for the fluorescent light was acting up. It could be something from a wall if you are set up close to one and the building folk have been working on the power. You might try plugging the monitor into a different outlet too.
You say you are getting headaches, check this out.
http://www.scn.org/help/monitor.html
