In a previous life many moons ago, I pushed wood through a table saw as an interim job (gotta pay the bills when a newlywed). Particle board is the potluck of all sheet wood. I even hit a #8 bolt once "PING" and whizzed by my right ear, no kidding. The biggest offender with particle board is the glues and formaldehyde. I'd look like a granola bar after cutting a few pallets of 1.25" 5x10ft sheets up for desktops and end panels through a 15HP sliding table saw with a 16" blade that would throw some serious dust, even with the guard and vac attached. To make matters worse, this shop was in a hot metal Quonset hut type building in sunny Florida... I'd loose so much salt my clothes had salt rings! And yes, talk about a rash...ugh...I'm squirming in my seat just thinking about it!
Some balsa has a camphor type odor to it, and that stuff does like you describe to me...stings my sinuses and gives a rash if it gets on my forearms. I guess it depends on how it was cured. Balsa is harvested as a dead heavy water logged wood, and usually floated down river to load up, then dried out which is when it gets light. I could be wrong, but I think it has a lot to do with what is in the water source that had soaked in before they dry it out and slice it up.
EricV