Do you have some sort of monitor that you can wear while you are doing physical activity? It is important to make sure that your heart rate does not go above a certain threshhold or you will experience dizziness, nausea, etc, even if you are healthy. For me, I find that I get nauseous if I go over 180 BPM while exercising, so I like to stay between 165-170 for a good cardio workout. Even 155-160 is adequate for a good workout for my age, but I like to really push myself. BTW I am 32. You can find charts of the recommended maximums by age on the internet.
I would also get checked out by a regular family doc to make sure that you don't have something else going on that is making you dizzy when you exercise. I had troubles whenever I had anemia.
How hard are you working out anyway? If you are having trouble with just walking or very light aerobics, that would be cause for concern, but if you're going full on and working hard, then you just need to learn to pace yourself a little better and not push things too hard.
It sounds like you have been tested to have a healthy heart. I would say firstly try to not push yourself so hard too fast. If I do I can actually get a bit of chest pain so slow and steady at first until you work your way up in speed. Also make sure that you are well hydrated when you run. It is possible you may tend towards low bp and that may be part of your problem. So I would say drink a glass of water before you start to work out and keep a water bottle with you and if you take breaks make sure you drink. Hopefully this should help but if you still have issues let your doctor know you have some sort of exercise intolerance and you may be able to be test while you are exercising to see what is going on. Take care.
Not knowing your medical history, my advice to you amanda is to first see a physician to determine if it's safe to push it. if you're good to go, get out there! A healthy heart responds quickly to physical demands placed upon it. So you'll quickly see the huffing and puffing subside.