Is falling plaster unhealthy ?

Hi Reggie! I'm in Virginia, too.I live in an old farm house- out in the Country in Richmond County ( Warsaw, Va.) Some of the rooms are shut off..plaster is falling- in those rooms. I estimate these rooms were created Waaayy before 1920's. My father grew up there and he was adopted in 1935. The house was standing long before he got there. A Historian estimates that this older part of the house was built around 1870??? I've lived there for 30 yrs myself and I have NO health issues & No breathing problems.I'm almost 53. Should I be concerned?? Plaster is just flat- no Stucco.

Nothing unhealthy about plaster unless you breathe large quanities of dust.
What you are looking at is lime and sand plaster reinforced with animal hair. Farmers used to shave animals when they butchered them and sold the hair in the farmer's market. Hair for plaster was still sold in Richmond up until about 1953 in Church Hill bottom. The lime in your house was probably made from oyster shells.