Thanks for providing more information.
Well most of the upper respiratory tract infections are caused by viruses and subside by their own in 7-10 days and sometimes cough can linger for few more days.
Even violent cough can cause strain in chest intercostal muscles resulting in pain.
Now as you have dull pain in chest with cough,deep breathing so possible cause may include Bronchitis,Pleuritis.
And you need to undergo chest X-ray,CBC,ESR and a clinical examination,chest auscultation by your regular doctor.
In the meantime you should take OTC Claritin and Motrin.
Do steam inhalation and saline gargles.
Take OTC Robitussin DM.
If your symptoms'll persist for next 2 days or get worse over the time then you should consult regular doctor for further evaluation and management.
If in case you develop severe pain in chest,upper right abdomen,shortness of breath then visit ER.
I hope this helps.
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