Stress is actually good for you, like for example your muscles, if they don't have any stress they atrophy and become weak. However if you stress them too much, too often they will remain sore, you will be in chronic pain, and never heal or get stronger.
The problem is really chronic stress, not stress itself, most disease is an adaptation to your lifestyle, with the exceptions of genetic disease or infections of course.
As your body is constantly regenerating, whenever you are damaging yourself faster than you can regenerate you are going to end up with lifestyle induced disease.
Stress is not just an emotion, there are actually three causes for stress: physical, chemical and emotional. Whenever your body is injured in a way regardless that it is an emotional, physical or chemical injury you are going to get a more acute response to any stimulus from the environment that could offer any threat.
For example if you broke a foot and you walk on the street with crutches, your perceptions and reactions to the world are going to be majorly changed. If you see someone running towards you, the reaction when you have a broken foot is going to be very different then the reaction if you would have two healthy legs because, when you are healthy it is easier for you to respond to that threat.
It would be a mistakes to say that that person has some mental illness problem, like a phobia for people who run. The acute emotional response is just a symptom of the injured leg, and because of that it can't be treated by itself because it is a symptom not a disease.
This is one of the reason why you will hear people say that their depression or anxiety got better when they changed their diets or start exercising etc. Because by doing so they eliminated some of their physical and chemical compromises, so they are better able to respond to emotional threats.