What should I do if I think I'm affected from inhaling asbestos smoke or dust?
If you believe that you have been affected from inhaling asbestos smoke or dust, you should visit a doctor. It may not be necessary to visit an emergency room or physician if you are suffering from minor conditions such as a headache, eye irritation, coughing, or sneezing. However, if you are having persistent cough, severe eye irritation, or more serious symptoms such as shortness of breath, chest pain or discomfort, or lightheadedness, you should visit a doctor.
This is particularly true for individuals who have had significant exposure (including a confined-space exposure or a facial or nasal burn), as well as for individuals with preexisting lung or heart conditions. If you have heart or lung disease, you should consult your doctor about any additional precautions you should take before helping with the rescue effort.
Courtesy of The Center for Disease Control.

Tips for protecting your lungs from dangerous asbestos inhalation