My mum has a hard red bump at the bottom of her leg, no hairs growing out of it and gets very red when she walks and puts pressure on it.

Possibly a boil: I can't tell for sure what the red bump is without gathering more information from you. Common things being common, it may be a skin abscess or a furuncle (boil). Boils arise when areas of skin containing hair follicles are exposed to friction and perspiration. Small ones may resolve with warm compresses. Larger ones need incision and drainage of pus. She should probably see a doctor.