There are two main reasons for the pain in the chest and shoulder: 1, it may be an acute myocardial infarction, which may cause pain in the chest and the back of the left shoulder. For example, lifting and carrying heavy objects, exerting too much force or moving for a long time may lead to local injury or strain on the pectoralis minor and pectoralis major muscles, as well as the supraspinatus and deltoid muscles in the shoulder, resulting in inflammatory edema and stimulation of the peripheral nerves, leading to pain in these locations.