Hi, it will be difficult to make a diagnosis from the picture. The bluish discoloration could be due to an allergen. It could also be due to circulatory problems, temperature problems or a rash. You will need to see if any allergens are triggering this reaction. You may also need to notice if ‘cold’ is precipitating your symptoms. You will need to consult your primary care physician for proper assessment. Regards.
Your hands changing color when you are cold or stressed sounds very much like common Raynaud's disease. Look it up and see if that is what you experience.
As to the pain in your left chest and left arm, when does it happen.
While you are inactive or upon exertion? Walking up hill or up steps?
You might describe it better. At some point, when you see a doctor, you need to be able to describe to him/her when the pain takes place and how long it lasts.
The two items, hands, and chest, may not be related.