I'm not going to say that smoking marijuana is awesome for your health and can't possibly cause problems, but I very much doubt it's causing heart problems. What you're describing, at your age, is most likely a panic attack. A lot of people get them when they're smoking weed, and of course, you're going to think you're having a heart attack.
I'm not going to tell you to quit - that's up to you. But it sounds like weed may be causing you more problems than it's worth, so why not try not smoking for a week or two and see how you feel?
It would not be hard to determine if you have a heart problem, but no one can do it over the internet. Here are some things that need to be done at your doctor's office:
1) check pulse/blood pressure: Ideally he will check blood pressure in both arms (though this is rarely done), and check your pulse at several sites (he may do this while he is auscultating)
2) auscultate (stethoscope): He should listen to your heart at a minimum of four places: right under your clavicles on both sides, and at the mitral/tricuspid sites which are around the area of your left nipple.
3) have an EKG: If he doesn't take you seriously, he might not order this test. However, it is a very simple procedure that is often done in the doctor's office, and there is no reason he should deny you (unless maybe your insurance won't cover it).
4) have further testing if necessary
You can check your pulse right now in a bunch of different places, but that will only identify a few potential problems. Here's how:
Radial pulse: Press on the radial artery on your wrist, thumb side... count the number of beats in 15 seconds, multiply by 4. Compare to the other side.
I was writing up a little guide on how to check carotid pulse and point of maximal impulse, but really, you'd need to see a doctor. The reason you would take more than one pulse is because sometimes the heart gives off an untransmitted beat (these are detected well with auscultation, and/or EKG). Or sometimes you have blockage in one of your arteries, so a beat will be felt more weakly in one than another. It is not likely that your arteries are clogged at your age, but sometimes there are other reasons for this (anomalous cervical rib, for example).
You should be able to tell if your pulse is regular, but again that needs to be interpreted by a doctor. Examples of irregular pulse include: irregular rhythm (note that breathing will affect rhythm slightly, no one has a perfect, unchanging rhythm), paradoxical pulse (untransmitted/weak pulse in the radial artery while inhaling), pulsus alternans (da dum, DA DUM, da dum, DA DUM), so on.
Still see a doctor, and still consider giving mary jane a break. But really, I haven't yet met someone who actually had a heart attack from smoking weed (especially at your age). It is almost always psychological - though I can very well understand your concern, and you shouldn't ignore it. I did meet someone your age who really might have had a heart attack from smoking weed, and I was very tempted to find out who his dealer was because it must have been some good stuff

But he was an amphetamine addict, and an anorexic as well - so those factors were more likely to be responsible than him taking the strongest bong rip ever, though again, I don't think the marijuana helped either.