The word in the chicken world is that chickens don't get colds. Ever.
If the chicken is sneezing, it could just be something tickling it's nose.
If it was my situation, I would pull the chicken and put it in sick bay. It may need a few days of warmer temps (inside), fresh acv or vitamin water, and clean food to feel better.
I would watch the other chickens that it roomed with to see if any of those chickens had a runny nose.
Was a snotty, running nose or possible food or water dripping down the nose? Edited - nose should be beak.
While I have considered eating a chicken that was in sick bay, my chickens recovered and went back out in the world. I have had SEVERAL (more than 2) chickens that just needed some down time away from everyone else and their life as a chicken. Seriously. A day or two or a week in sick bay and they fully rebounded.
If you and your family are healthy and not worried about catching the avian flu, I would say harvest and make sure the chicken is cooked very well before eating.