This could be muscular tension, too. Do you work at a computer, did you lift something heavy, practice yoga or work out? Try some stretching and deep breathing and relaxation visualizations for a few days. Good luck!
The answer depends on whether you feel like the pain is in your breast tissue or deeper than that. The heart lies just beneath the left breast, so if you are having pain there, it should probably be checked out. Women often don't have the typical crushing chest pain associated with heart attacks or coronary blockages. Chest discomfort can present in many ways, including numbness/tingling in the left arm. It wouldn't be a bad idea for you to at least be evaluated by a physician -- have an ECG, maybe a stress test.
I wouldn't run to the ER. It is normal to feel like a tingly/itchy sensation under the breast tissue. The going numb part is what worries me. Don't go to the ER, but do call you family doctor or your ob/gyn if you have one.