can a common cold come with diarrhea?

[TMI ALERT]
i've recently come down with a fairly light cold, doesn't have a shitload of mucous but a decent amount. problem is i have really bad back pain which makes coughing/sneezing near impossible. nearly no mucous is being expelled in the proper way because of my other condition(unrelated to cold, never has given me the runs just makes coughing and sneezing hurt like hell)

anyway tonight i've been feeling very off in the stomach, there's been a decent amt of mucous in my stool.

anyway my questions are, can a common cold cause diarrhea?

should I treat it like a stomach flu and avoid food all together, or eat dry bland absorbent shit like rice n toast?