This definitely sounds like SVT (Don't worry this isn't dangerous just annoying). Unfortunately it's difficult for doctors to see what's happening unless you are having an episode while there. I suffered from SVT from the age of 14, when I described it to my doc he gave me an inhaler. Finally when I was 20 I went to A&E with the palpitations that allowed them to track my heart and refer me to a cardiologist. My advice is to head to A&E next time you experience them, not because it's life threatening but it's practically the only way you can get it recorded! Also, look up the valsava maneuver online this really helped me to manage my palpitations.
Does it feel like it takes off really fast in what feels like one heart beat and then goes back to normal? Have you been able to track how fast? You may need to go back to the doctor and tell them when it is going fast it is hard to breath and that it starts and stops suddenly. There is a condition called svt that is caused by extra muscle tissue in the heart allowing the heart to get caught in a reentry circuit. Or you could have something called inappropriate sinus tachycardia or something else. It seems to me that you should at least try to track what is happening with a monitor. If this happens every day a 24-48 hour monitor should catch it. If not then ask for a 30 day event monitor to try and record what is happening. Once it is recorded the doctor should be able to tell if you have svt or something else. But sometimes we need to go back to doctors when our symptoms do not go away. They often write things off as stress initially to see if they go away and we just have to go back and insist that the issue get investigated further. Just because you are 15 doesn't mean you shouldn't be looked at proper so just go back and insist more tests be done. If you do have svt there is a fairly easy fix with an ablation. IST may be harder to treat but treating it would be better than not. If your current doctor will not help you then find another. Best of luck sorting it out and keep us posted on what you find out. Take care.
Some times it can be anxiety, or panic attacks. These can happen out of the blue and make you feel terrible. Fast heart rate,dizziness fear. And the more we worry the worse it gets. Just a suggestion .But if it keeps happening ask your doctor for a referral to a specialist. Can your parents help.