Answer
There are two health risks from asbestos exposure - chronic inflammation of the lung and lining of the chest cavity (asbestosis), and possibly lung cancer (mesothelioma) a decade or more after exposure. For asbestosis, there is no need to see a doctor unless you have noticeable lung or breathing problems. For lung cancer risk, it would probably be a good idea to be tested by an oncologist now for any signs of cancer, and then continue testing maybe every five years or at some other interval recommended by a doctor. There are bunch of government programs for health problems related to asbestos, so some testing might be covered (first link below)