I think that nails are abiotic because they are made up of dead cells, and they do not need to be taken care of they only need to be cut and that won't hurt us.
Hair is biotic because it is made up of dead cells but were once living cells. Biotic things are ones that are alive or were once living. The same goes for fingernails, their cells were once living therefore they are biotic compounds
Nails are colloidal, and no pain point, of course, when the cut will not hurt . Human skin can feel pain is because the skin there are sore spots.