If I have shortness of breath after short exercises do I have bronchitis?

Not necessarily... Acute bronchitis is caused by an infection of the airways and you would have symptoms of infection. Chronic bronchitis is a form of COPD and is usually due to cigarette smoking. This, too, would have other symptoms and not just decreased exercise tolerance. See your doctor to evaluate your decreased exercise tolerance, if present.
No. This really depends on your health history and the details of the symptoms you are having. You should start by seeing a doctor for a physical examination, and the discuss the possible cause then.
R/o asthma. Should get evaluated for exercise induced asthma. Also would rule out exercises induced hypertension or occult hypertension.
Probably not. Shortness of breath with exercise can come from lung disease, heart disease or deconditioning. It is important that you see a doctor as soon as possible to get an exam and some testing to figure out the cause. At 24 years old it is unlikely to be from your heart. More likely would be asthma or reactive airways. Bronchitis is an infection of the bronchial tubes causing a deep cough/congestion.
No. Not likely. You are most likely suffering from exercise-induced bronchospasm, which is more related to asthma. This is treated somewhat differently from bronchitis.