I am finishing a course of antibiotics. it has been a week and i don't feel any more cold sypmtoms but i still have a cough. the constant cough produces mucus.

Post-tussive cough.: When we're sick with an upper or lower respiratory infection, the cough tends to be the last symptom to clear. This is called a post-tussive cough which, as you can surmise, means "post-cough cough". The coughing itself makes the cough linger. The solution? Cough suppressant.

Follow up with MD: generally antibiotics not for cold (viral), but for bacteria that can arise in setting of cold. Mucus production can be in setting of either, but green or dark yellow mucus suggests possible bacterial infection. See your MD for followup if prolonged, shortness breath, hi fever, blood in sputum, nausea/vomit, and other red flags beyond a lingering cold. I assume no history of asthma or smoking.