Hello from JustAnswer. This is Dr. Love and I will be assisting you today.
It will help if you could provide some further information.
Are you having any shortness of breath, particularly shortness of breath that is present between coughing spells?
Are you taking any chronic medicines?
I had asked for some further information and have not heard back.
There are several possibilities of how a cold can progress to causing chest symptoms such as you describe.
The most common situation is that a viral upper respiratory tract infection will directly spread to causing a viral bronchitis, an infection of the airways of the lungs, which can cause significant coughing. It is also possible for a viral infection to cause inflammation of the lining around the lung, which is called pleuritis or pleurisy.
However, another possibility that would be more of a concern would be the development of pneumonia, an infection of the lung itself. If you are having significant shortness of breath, then that would be more of a concern. If you are having significant shortness of breath, then it would be important for you to be seen by a doctor soon.
If there is no shortness of breath, then it would be reasonable to continue managing this at home. A cough syrup can help to ease chest symptoms, such as guaifenesin plus dextromethorphan. For the pain and shock sensation, it also may help to take an over the counter anti-inflammatory medicine, such as naproxen.
If I can provide any additional information, please let me know.