Your description sounds like sleep apnea, a common condition in which breathing stops during sleep. It may be helped by making sure that you never sleep on your back, but you really should be checked out by a sleep specialist physician. Over the long term, sleep apnea can have life threatening consequences.
Does your breathing get slower and slower as you relax towards sleep? Does it seem as if the act of breathing changes from an involuntary function to one that is voluntary? In other words, you need to make yourself breathe or else you will stop?
Does it seem that as your breathing slows, so does your heart rate slow to an abnormal speed? Are you concerned that falling asleep may mean not waking up?
If you answered yes to these questions, then I can relate to your situation, but don't have any answers. I suspect that it may be lung damage which could lead to a possible pulmonary arrest, or cardio-pulmonary arrest.
My theory is that it could be lung damage as a result of chemical exposure. I find that since having this issue, I am highly sensitive to chemicals. Even the smell of paint now sometimes makes me feel as if I am going to collapse. I would suggest staying away from any and all chemicals as a precautionary measure, including chlorine, (or other pool chemicals) pesticides, sunscreens, DE powders, insect or animal repellent, etc. If my theory is wrong, I certainly don't think you'll be any worse off by avoiding chemical exposure. I find that my condition is made much worse if I spray Lysol in my home. I have had much difficulty breathing after its use. I would strongly suggest staying away from it.
If you haven't already done so, you may want to visit a pulmonologist, and/or cardiologist. They'll probably look at you like your crazy, but it least then you can rule out the possibility of other disease.
Hearts and lungs can both heal if damaged, and can be strengthened with exercise. I don't believe cardiovascular exercise such as running, cycling, jumping rope, etc. can pose a problem. On the contrary, I believe it's the most important thing we can do to strengthen these systems. But a visit to the doctor beforehand is always a good idea just in case there is something there that they can actually find. Just don't get your hopes up about that one.
Don't "give up". Press on. You may have a problem, but problems can be solved. But you need to first identify the problem before you can begin solving it, and this often requires much troubleshooting, and reductive reasoning. So, you've got a lot of work to do. Start testing different things to see what improves it. Avoid doing the things that seem to make it worse. Pay attention to EVERYTHING. Giving up is a cop out, and should never be considered a viable option. If you're not important enough to yourself, consider that someone close to you probably is important enough to keep pressing on.
Go exercise, get some sleep, then get back to work, figuring this thing out.
Youll have to elaborate a bit on your situation.
Hope I can help