I don't think the snot running from your nose is your body flushing out anything. I think it's the cold trying to propagate itself.
I often use off the shelf allergy medecines to stop the flow. It allows me to get on with my day without having to "trumpet" my nose every 10 minutes.
The rest of the advice is sound. Get your sleep, rest, eat sensibly. A cold usually lasts 4-5 days and there doesn't seem to be much you can do other than last it out.