You speak of a 'cool down' but to be honest, that speed is not a cool down.
When you start using the treadmill, you should start off with a walk and build the speed up slowly to allow the heart to gently respond. If I jump up off the sofa and start to sprint, then there is a much higher risk of my heart going out of rhythm. When you cool down, you should slow down to a walk for about 10 minutes. This also allows the body to remove all the toxin build up from muscles in the body. I'm surprised you dont suffer from cramp.
Anxiety can cause chest pains, even though there is nothing wrong with the heart. The sudden burst of hormones/enzymes can over excite the heart. If you had heart problems, you would certainly feel it while using the treadmill. With regards to your eating, this is more common than you think. Even trapped wind can cause feelings which convince you that your heart has a problem.