I have asthma and allergis, but big lungs. I workout as often as I can but but I get sick all the time. What can cause this?

Exercise asthma. You may have exercise induced asthma, where increased airflow through the airways causes bronchospasm, mucus production with coughing and wheezing at the end of exercise or 5-15 minutes after completion. It can be blocked with 2 puffs of albuterol prior to exertion. If exercise is outdoors, you may need to add an anti-inflammatory med, such as an inhaled corticosteroid.
Possibilities... Do you mean you feel sick while exercising? If so, it could be related to exercise-induced asthma. You may need a bronchodilator inhaler prior to exercise and perhaps when you stop exercising to prevent this. See your doctor for evaluation and treatment. If you smoke, you need to quit as this can cause airway inflammation which can lead to infections.
Need more info. "sick a lot", ?In lungs....If so may have inadequately tx'd asthma... Leading to further lung damage. Either way f/u with your doc until the root cause is determined.