Thank you for the query.
What are you suffering from is most likely intercostal neuralgia
due to rib nerves compression. According to your symptoms, some rib is irritating such nerve. The pain aggravates while chest is moving. As you have noticed, the best way to get rid of it is stretching (looks like it works for you).
However, always when the chest pain
appears, heart condition should be checked. You can do that with heart ECG.
Hope this will help.