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It sounds like your cat may have chin acne. Usually people will notice black stuff on the chin, maybe with a little hairloss. Sometimes the area can get infected and swollen, necessitating the need for antibiotics. Most chin acne (if no infection) is due to an allergy or sensitivity. If you currently use plastic food or water bowls, I recommend getting a ceramic or stainless steel one and washing it frequently. Using an ointment containing benzoyl peroxide can also help by opening up the pores.
My other thought, if the dark spots are flat with the skin, is just pigment. Particularly in orange or calico cats, they can develop more pigment spots on their lips and gums as they get older. These would cause any imflammation, however.
Does that help?