get a pro to check for mold... it's wicked stuff, I've got a friend who's got it in her lungs now and it is ruining her health, very hard to treat... do NOT do mold cleanup yourself, if you stir it up and get spores in your lungs it can be very serious.
headaches are a clue to oxygen issues (CO2, leaking flues, burn fumes, oil fumes, etc.) if you can smell the fuel oil, it's leaking or the flue's leaking.
if you're stuffy, sneezy, respiratory issues without the headaches, it's more likely to be other inhaleables (dust, mold, dander).
and you have my sympathy on the moving issue. the guy we lease from just put the house on the market. we have 4 months to find somewhere for goats, sheep, horses, dogs, cats, and all sorts of poultry. blows the heck out of my garden plans as well.