How to tell if you have fibregl in your home?

My landlord tells me that my loft in my 1960s home is pretty dusty with what he thinks is fibregl dust. What I was wondering was that on very windy nights the lid to my loft (which is not boarded or insulated) blows off and I was thinking that if it blows off then fibregl dust must be going into my home, (I hoover my home frequeently with a Dyson filter hoover) but I was wondeirng hyow would you be able to teel if there was fibregl dust in your home?, does anyone know, also if there was fibregl dust in my home would we be getting skin reactions o something? Thanks