mesothelioma is actually fairly more uncommon than lung adenocarcinoma in patients exposed to asbestos. So you're more at risk for a lung tumor than mesothelioma which is a tumor of the tissue surrounding the outside of the lung. I would just tell your doctor that you found out you had an exposure, which would just let them know to screen you better, such as an annual chest x-ray or perhaps a CT.
Also given your 8yr history (if its just 1 pack a day, an 8 (8 x 1) pack history doesn't put you at high risk) I'd suggest you get screened. You'd need to be smoking 3 packs a day to get a 24 (8 x 3) pack history... (basically, high risk is over 30).
As far as asbestosis, which is an inflammatory lung condition, your primary care physician would not handle this, and you'd need to see a pulmonologist, a doctor who specializes in lung disease. You'd need to do some functional tests to make sure your lungs work.
But take all of this with a pinch of salt. You only had one exposure, this wasn't a daily routine for you. I would still follow through with your doctors though.
Above all else, do not smoke.