I got exposed to asbestos some 25+ years ago at Hughes Aircraft and was on annual monitoring for lung capacity. It wasn't a big deal, but it did take a little out of you trying to keep the ping pong ball high enough up the tube. It was like this opening sequence from The Right Stuff. I dunno, your doc may want something more extensive.
While I was employed elsewhere, the part of Hughes I worked for got bought by Boeing. When I got hired by Boeing some 11 years later, my health screen warning and monitoring program was waiting for me and I had to start the whole thing over again.