Bad EGR valve?

My check engine light came on a while back. Every so often, the car would give a little sputter but then seem to straighten itself out again. About once a week or so, it would shut off when I'd come to a stop. It would start right up again though. Took it to AutoZone and the error was something about insufficient EGR flow. I did some checking online and found some people said all you have to do is remove the EGR valve and clean it out real good with carb cleaner. Did that and it actually seemed to run a little better for a while. It's back to doing it again though. In addition to the EGR valve, what's that piece that almost sits on top of it (has a hose running from it into the EGR valve). Also, could a bad oxygen sensor cause these symptoms too?