A cold involves a runny nose.
A flu involves a runny nose and fever.
A chest infection or bronchitis (maybe after a cold or flu) involves a constant cough.
A sinus infection after a cold or flu is where your nose has stopped running for a day or so, but you are totally congested, your snot is dark yellow or green, and you may have a headache. This backup can go down your throat and infect your chest too.