Yes the pains would not go away if it was a heart attack, not until the heart muscle concerned was dead. As well as seeing the Doctor, which is good advice from the above, I would recommend some gentle stretching exercises as a part of your regime. It is important to warm your body up before any exercise because exerting cold muscles can cause discomfort. Before going on a run I used to do 3 minutes of gentle star jumps. This not only warms the muscles, but slowly speeds up the heart rate and gears your arteries ready for the run. At the end of a run it's just as important to slow down gradually. I used to just walk fast for the last 200 yards and then slowly walk for 5 minutes to allow toxic wastes to exit the muscles, and let the heart slow down more gradually.
I agree that you should see a doctor about this.John is absolutely right; stabbing pains are not heart related. Having a heart attack at your age is about nil, however you may have something called hypertrophic cardiomyopathy. This is extrememly rare in someone your age and the chances of this being the problem are about zero, but it should be looked into. Also asthma can cause the problems as you describe so that needs to be looked into. Good luck
This really does not sound like it's related to your heart. Stabbing pains that are short in nature lasting only seconds or a minute or two or increase with breathing are almost never cardiac in nature. Chest pain from a heart attack is more often a pressure or squeezing pain.
Having said that, anytime you experience chest pain you need to get it checked out, although rare in some one your age it is remotely possible so see your doctor or if your symptoms worsen I would encourage you to go to the hospital to be safe.
Jon