I'm going to start of by saying I'm a biologist, not a doctor. This comes from my knowledge of biological systems, not from my limited knowledge of medicine.
I don't think you would have damaged your heart by running through a cold. The cold virus simply doesn't affect your heart under any circumstances I can think of.
There are a few options I can think of however. If when you thought you had a cold/flu, you had pnuemonia, lung damage could have occured. If you did have mono, the virus is still in your body. While its relatively rare, the virus could resurface and cause symptoms again. This usually occurs under times of stress when your immune system is weak and can't keep the virus in check. You mentioned that you think your colds are caused by stress, so this could be related.
Additionally (this is a super simple, not totally accurate, but pretty good metaphor), if you've had alot of illnesses in the past, they could deffinitely still affect you today. Assuming you're viewing letsrun from a PC, you've probably had a computer virus. Your antivirus might've cleaned it, but your computer was never the same again. You've probable had a bunch of viruses that make changes to your computer that you don't even know about, and even though they get taken care of, the effects add up.
A similar thing happens to your body. Most infections you don't even realize you have. Viruses can stay in your body forever without any noticable symptoms. They can cause damage that only becomes apparent under certain circumstances. Viruses can cause anything from colds, to fatigue, to cancer.