First and foremost this is really something you should see your doctor about. I had something like that a few weeks ago. I seriously thought I was having a heart attack (even though I am only 21 years old), but it turned out that I just had inflammed cartiledge(sp?) in my rib cage called costochondritis. I would have these on and off bouts of sharp pain in my chest that felt like someone was stabbing me. Like you said, my pain would sometimes last only a few minutes. Ever once in awhile it wouldl last longer. Is there any swelling around your rib cage? Also, if you press down on your rib cage do you feel the sharp pains? I found movement that I didn't do all the time (like taking a deep breath) would cause the pain. Have you had a cough recently or done some awkward movements like lifting? That is what the doctor asked me and it turned out that is what caused mine. Like I said go see your doctor because they can make a definitive diagnosis and help you get better.

Feel better. Hope this helped.