I have a pimple that looks like it has dead skin and a brown circle around it is this a staph infection?

Hyper pigmentation. Post-inflammatory hyperpigmentation, which is a darkening of the skin pigment due to increased amounts of melanin, usually occurs during the healing process after the treatment of a skin disease or acne. While most cases of post-inflammatory hyperpigmentation disappear on their own after a few weeks some can last for weeks or months.