Hi, about six days ago, I got my nose pierced. After a few days, I've noticed that I had a runny nose, sore throat, and a slight cough, which has recently got worse. So, I was wondering does getting your nose pierced cause sinus problems, even after a few days that you get it?

That is more indicative of a viral infection. Which is to say a common cold rather than the result of a facial piercing. I am assuming that your keeping the area around the piercing dry and clean? There isn't any soreness or redness or other signs of an infection?