The problem is, it could be near impossible to test for something when you dont know what test to perform, so its a lot easier when you have some idea of what the source is and therefore what the chemical could be you are trying to measure.  For example melting plastic, burning rubber, new office furniture, a chemical process, water drains, soil, refuse piles.  In this case you might be able to self diagnose using a Gastek polytec tube method (http://www.afcintl.com/deluxe-hazmat-detection-kit-from-nextteq-6.aspx) with reasonable results.

But in absence of any information whatsoever there are tools which can measure and detect unkonwn chemicals in the air (such as those used by the fire brigade eg. https://www.perkinelmer.com/lab-solutions/resources/docs/PRD_Torion-T-9-GCMS_012311B_01.pdf) based on chemical libraries - expensive to buy, but possible to hire?

If its a gas, you may be able to take a "grab bag sample" and send this off to a lab (again though they would prefer to know what it is likely they are measuring for), or absorb it on to a charcoal sample such as tenax tube, (for example a top 10 or top 25 solvent screen) however in these cases you still need to have some basic idea of what it is you could be sampling for (the volatility of the solvent for example may impact the choice or tube to use).

The above links are just straight from google, but if you need a recomendation of a company who are helpful and good at problem solving- I have found SAL ltd. very good, though I think they have recently changed their name (no commercial link).

Even with gas chromatography–mass spectrometry equipment you still need an idea what you might be looking for.  It’s what I call the tri-corder effect, where as in Star Trek, you just point a probe at something and it instantly tells you what the stuff is and what it can do to you.

To narrow it down you need to identify the source- is it something burning, vapour coming off new carpet tiles etc.  If the source is not obvious it can be a real pain to identify what you are looking for.