I am easily irritated, but I don't feel sick. Can than be an illness?

Yes. Irritability can be a symptom of a number of medical conditions. It is a common symptom of depression, anxiety, or bipolar disorder. Sleep deprivation caused by any condition can make a person irritable. Withdrawing from nicotine, caffeine, alcohol, or other drugs can cause the symptom. Chronic pain or stress can do it. So can an overactive thyroid or a hormone imbalance. See your doc.
Need more info... Are there any other concerns. Are sleeping ok? Is you energy too high? Do people tell you - slow down? I guess if you are seeking the answer, it bothers you. Why don't you see a psychiatrist who could help you to sort out your problems? Sometimes people don't feel sick, because the illness may trick you....