My dad has severe black fungus Under his toenails. I have tried to cut them down I didn't wear a mask or gloves do I need to worry about inhalation?

No. The kind of fungus that grows on fingernails and toenails is very different from the kind that causes disease when inhaled. Environmental molds in buildings and natural spaces which become airborne can cause respiratory illness; these molds belong to a different class of fungus. But your dad should perhaps seek medical treatment to rid himself of his infection.