I've had a bad sinus infection for about a week. now i'm coughing when i drink cold water?

You may be congested: If you're still recovering from your sinus infection, you might still be congested. So usually when you swallow, it's difficult to breathe at the same time, and you may end up coughing with your post nasal drip, if you're still having thick discharge and sputum. See you doctor, if the discharge has become colored, and if you are coughing more often.