Hello and thanks for the question.
The metallic taste could be from infection (and hence the cough). However, a metallic taste in the mouth can be from several things. First thing is to consider the fact that many medications can cause the taste of metal in the mouth. Some of them include, Captopril (for blood pressure), Flagyl (antibiotic), Metformin (diabetes medication), Auranofin, the contrast dye used in CT scans, antidepressants, heartburn medications, and low calcium treatments.
Also, unhealthy oral conditions can also cause a metal taste. Gum disease, and abscesses teeth can lead to this taste as well.
Other causes could include peptic ulcer, food allergies, lead poisoning, selenium toxicity, copper overdose, too much calcium in the blood, mercury poisoning, acute kidney failure, burning mouth syndrome, lichen planus, and even cancer (listed from most likely to least likely).
Most cases of metallic taste in the mouth will come and go without known cause and will resolve on its own and most cases are not serious. Brushing your teeth multiple times per day and also brushing the tongue, eating with plastic utensils, and avoiding things like Rolaids and Tums until the problem resolves will usually help. If the taste continues, you should see your dentist or regular Dr for an examination and diagnosis.
You can fight against the metallic taste by having citrus juices, lemonade and foods marinated in vinegar. They not only break through the taste, but also help in saliva production that helps in washing away the metallic taste. Also, you can also try rinsing your mouth with a solution made of a teaspoon of salt and eight ounces of water.
If your cough does not improve very soon, you will need to make sure the cough is not related to the metallic taste (to rule out infection).