Chronic cough is one of those unfortunate problems that seems to happen regularly. In general, things that would make you go see a doctor
include any changes for the worse, any fevers above 101F, coughing up blood, weight loss
, pain, or other problems. As long as there are not other symptoms other than your intermittent cough, and provided that you are otherwise healthy, you can have a cough for up to 3 weeks that is still considered an acute cough, such as what comes from a cold or other upper respiratory tract infection. After 3 weeks, it is considered a subacute cough, and a visit with your physician would not be inappropriate. It is likely to be caused by post nasal drip from your cold that is causing inflammation at the back of your throat, leading to the cough. Warm teas and water break up the mucous, and help you feel better by soothing your throat. Some over the counter anti-histamines also can help to decrease the amount of mucous that your body is making, and might be worth trying. Asthma
and GERD (acid reflux) are other common problems, but don't sound as likely given what you are describing. Chronic coughs last more than 8 weeks by definition, and should be seen by a physician. Finally, if you have a smoking history, family or personal history of lung problems or other medical conditions, you should see a doctor sooner rather than later.