My one-month-old kitten has no fur under its armpit and red skin; what is wrong?

Hair loss, inflamed skin, and small black dots under a kitten’s armpit may be: first, bacterial folliculitis from excess oil and bacterial infection causing loss and redness; clean and disinfect the area and apply antibacterial medication.

Second, parasites such as flea dermatitis, where the black dots are flea feces. Deworm both the kitten and the mother internally and externally, and disinfect the home regularly.