Not sure about the cold as I don't think my DD has ever had one, but the runs might be related to teething, mine gets REVOLTING poo for 1-2 weeks before a tooth eruption- the poo isn't watery but loose, massive and foul smelling and creates a bad nappy rash too. I try to clog her up with bananas, bread etc but it just has to run it's course. It drives me to the brink of insanity though, as she tries to run away every nappy change.
Hope your baby is feeling better soon, sorry if I have steered you off on the wrong course with the poo but every time we have bad poos it is teething related.