Do you have any information on pesticides used in rental homes/apartments and the rights of the renter?
Your concern about the pesticide used in your apartment is valid. As the tenant, you do have certain rights. Keep yourself informed about pest control without pesticides so that you can share information with your landlord and neighbors.
What I recommend is that you contact the exterminator directly and ask for a copy of the Material Safety Data Sheet (MSDS), which they are required to have by law. The MSDS will give you very detailed information about the active ingredient in the pesticides used. However there are also “inert” ingredients which may be harmful as well.
You can look at the pesticide fact sheets at Beyond Pesticide's website. From the main page, select Pesticide Fact sheets from the Info Services pop-down menu.
The Northwest Coalition for Alternatives to Pesticides also has fact sheets on their website.