I'm no chemist but it looks like you can get sample badges for recording chemical exposure "reasonably" cheaply ($75 a day approx)..
http://www.assaytech.us/pricelst.htm
Sure they are too expensive for everyone to do it all the time but it looks like it would be quite possible for someone to monitor their own exposure for a say a week - or perhaps just keep one badge until an incident occurs.
I guess the problem is knowing which group of chemicals to monitor. Perhaps..
http://www.assaytech.us/541_panel_sales.htm
"Who Uses This Panel: People who have an Indoor Air Quality issue at their facility, but do not know exactly what chemical(s) might be in the air."