If you can physically touch your neck, chest, or shoulder pain, or change it in any way by movement or pressure or heat or cold, then it is NOT heart pain.
The reason for this is the way our nervous system is formed in embryology.
Believe your doctors. You need specialized physical therapy, with particular emphasis on exercise and range of motion.n
First you get all the testing done by a (cardiologist or a heart specialist) that has to do with your heart (EKG, Electrocardiogram,stress test,x-ray, and whatever the heart doctor orders.If you feel like you need a second opinion get it, after all that is done then work on your posture, type of work you do as if you are using your shoulders to lift stuff up all the time you might be keeping your muscles from relaxing.Hence the pain.
You said it (Neck pain and shoulder pain compressed bone in your neck can cause other muscles around your upper torso to compensate for other muscles)
So first get checked then go from there for a piece of mind.Will keep you from worrying and anxiety about your heart.