Post-Inflammatory Hyperpigmentation (PIH): This is a common condition that occurs after inflammation or injury to the skin, leading to hyperpigmentation. Given the age and presentation, it's plausible that the hyperpigmentation is a result of a previous skin injury or inflammation, such as eczema or an insect bite.

Café-au-Lait Macules: These are benign melanotic lesions that can appear as hyperpigmented patches. They are common in infants and can increase in number with age.
Mongolian Spots: These are benign flat congenital melanocytic lesions that appear as blue or blue-gray patches, often on the lower back, but can appear on the arms. They typically fade by the age of 5.
Erythema Toxicum Neonatorum (ETN) Residual: Although ETN typically resolves within the first week of life, residual hyperpigmentation could potentially persist.

Child Abuse: It's crucial to consider non-accidental injury as a cause of skin lesions, especially if the pattern of injury is suspicious or if there are other signs of abuse.
Infectious Diseases (e.g., Congenital Syphilis): Certain infectious diseases can cause skin lesions and hyperpigmentation. Early diagnosis and treatment are critical to prevent long-term complications.
Malignancies (e.g., Congenital Melanoma): Although extremely rare, it's essential to consider the possibility of a malignant process, especially if the lesion is atypical or changing.

Neurofibromatosis Type 1 (NF1): Café-au-lait macules are a hallmark of NF1, but the presence of other diagnostic criteria (e.g., neurofibromas, axillary freckling) would be necessary for this diagnosis.
McCune-Albright Syndrome: This rare genetic disorder can cause café-au-lait spots, among other symptoms like polyostotic fibrous dysplasia and endocrine dysfunction.
Phakomatosis Pigmentovascularis: A rare condition characterized by the presence of melanocytic and vascular lesions, which could present with hyperpigmentation.