It is estimated that up to a third of patients with asthma
can suffer from respiratory problems after being exposed to agents such as lysol (ehow.com data) but it can happen even with people who have bronchial hyperesponsiveness on exposure to chlorine fumes.
Feeling drained of energy is not an obvious feature of asthma but if you are coughing and then feeling tired, it is recommended you visit a Chest Physician and get pulmonary function tests done to ensure your airways are normal.
A trial of beta 2 agonists (short acting ones) may prove helpful.
Discuss this with your doctor.
If you have any other respiratory allergies, please mention this as well.