Those could be symptoms of a cold coming on, or a flu. It could also be bronchitis. Whatever it is, it means you're getting sick, so get some rest and go to the doctor if it gets really bad.
A tight chest and cough would indicate perhaps an upper respiratory infection. It could also be bronchitis or asthma. Certainly it should be checked by a physician as soon as possible.
TIght chest and cough can be either serious. If it is a dry cough and tight chest it can mean bronchitis and should be treated by a doctor asap. Bronchitis can tunr into pneumonia real quick and it is so easy to die from pneumonia.
It's generally a sign that there is some kind of drainage at work, possibly infection in the lungs. Especially if the cough produces yellow or green colored mucus. A doctors trip will likely be needed to solve the problem.
