Here is what i think may be going on
The pain in the chest has many reasons but the most likely cause for the type of pain you are having are as follows
1) Extreme cough induce residual muscle pain
2) viral pleuritis
(mild infection on lung cover =pleura
3) costo-chrondritis (pain in the ribs)
(bacterial infection of lung super seeded by viral infection)
5) blunt Injury
to breast ?
1) If having FEVER
AND COUGH with colored (yellowish,greenish,brownish) please consult physician as it is as strong sign of pneumonia
2) If NOT HAVING COUGH/ FEVER it mostly an viral pleuritis- the its fine it will resolve on its on in few days mean while can take pain medication and will go away in 5 days or if still their is persistent pain after five days consult physician
3) Any sign of pain while touching/pressing on the area indicates ribs pain (costochrondritis)/ muscle pain, pain medication will be good for it can do some warm water sponging might help.