I have been coughing for a week now. it started with an irritation in my throat. it is not dry cough there is mucus. i also feel heavy in my chest.

Avg cough = 18d: A recent study concluded that the average duration of a cough illness lasted approximately 18 days. So the bad news is that someone who's been coughing for a week has another 10 days of cough left on average. However, if s/he is feeling short of breath and/or having fevers, sweats & chills, it's best to go see one's family doc. Antibiotics aren't warranted for every (cough) illness.