Thanks for your question.
Numbness of the arm and chest are not typical for cardiac disease, and it's good to know that your EKG's have been OK. To completely rule out the heart, I would discuss the possibility of a stress test, and if this is OK, then other causes have to be considered.
Should your heart be ruled out as a source, I think the next logical place to investigate is your spine. Nerve problems can cause burning pain and numbness. Regular X-rays should be considered, and if normal, then an MRI of the cervical and thoracic spine would be next on the list. In addition, a chest X-ray should be performed.
If everything continues to come up negative, a consultation with a neurologist would be a good idea for their evaluation of what the cause is. In some cases, people develop pain and no cause is found and we are left with helping patients by treating the symptoms, in this case chronic pain, for which there are several options available today.
So, make an appointment with your doctor to discuss what more can be done to find the cause of your symptoms.
Best wishes and feel better.
Martin Cane, M.D.
Here are some articles that might be helpful for you:
Chest Pain (overview)
Symptoms of a Heart Attack and Stroke