Hi,
Thanks  for  your query.
Left side 
chest pain is what we are always afraid of as heart issues can give such symptom.
However if the pain has appeared suddenly with 
shortness of breath and someradiation to the arm, 
pneumothorax is possible. This condition can appear with no reason. Sometimes sudden cough or sudden lift of heavy object can cause it. It is more possible if you smoke or have chronic lungs disease like 
asthma or 
bronchitis.
If nothing like that is present, strained muscle is the most probable reason. Strained muscle usually appears only when the chest is moving, and should be completely gone when lying down and not breathing. 
If the pain is sharp and well localized, more intense when breathing, rib nerve issue is the most probable reason.
In both cases, rest and anti-inflammatory medicines like Diclophenac should help.
If the pneumothorax sounds possible, you should have chest x-ray done as soon as possible
Hope this helps. Let me know if you have any more concern.
Warm Regards.