Hi M.,
As you can see from what other's have written there are a variety of ailments -- serious and nonserious -- that can cause chest pain. Your doctor is the best person to evaluate this pain. If you feel s/he is not treating you and your instinct tells you something is wrong, seek out another doctor and get a second opinion.
As an alternative, the next time you have pain of the kind you describe, go to the emergency and inform the triage nurse that you are having chest pains radiating to the left. This will trigger an immediate evaluation for a myocardial infarction. The hospital should run and ECG and take blood to evaluate cardiac troponin levels (either I or T -- both tests are equally reliable). Elevated troponin is an indication of heart damage. If the ECG and the troponin do not indicate a heart problem you can at least stop worrying about this aspect.
Did the doctor do any follow up at all? I assume s/he checked regular vital signs (pulse, respiration, blood pressure and probably even ran and ECG, which would be according to protocol for someone with your complaint). Did s/he order any kind of tests? If so, what, and what were the results? Did he tell you what s/he might suspect is causing the pain?
BTW, short pain like you're describing is not likely to be cardiac induced. Cardiac pains of concerned usually last for hours. This sounds more like a muscle spasm in the chest wall. How frequently does this happen? Have you had the pain for a long time? Have you done anything lately that could have cause muscle injury or fatigue? As your kids get bigger and heavier, a sudden lift or twist that wouldn't have bothered you before could cause a minor muscle sprain or tear. When my oldest was three, he was bouncing on my chest while I lay on my back and I was also lifting him up in the air. The next day I started to have chest pains and couldn't breathe. An evaluation in immediate care ruled out a heart problem and the diagnosis was a bruised sternum (breast bone) and muscle sprain. BTW, even though this is what turned out to be the cause of my pain, I am in no way suggesting that this is the cause of yours. Each case has to be evaluated independently.
I hope all turns out to be well!