Erythema Toxicum Neonatorum or Infantile Acne: These conditions are common in infants and can be exacerbated or appear during teething due to hormonal changes. They typically present as small, erythematous papules or pustules on the face, but can also appear on the torso and back.

Contact Dermatitis: This could be due to irritants in soaps, lotions, or other products used on the baby's skin. The rash typically appears as red, itchy, and sometimes blistered skin.
Atopic Dermatitis (Eczema): Although more common on the face, arms, and legs, atopic dermatitis can appear anywhere, including the torso and back, especially in infants. It's characterized by dry, itchy, and scaly skin.
Heat Rash (Miliaria): Caused by blocked sweat glands, this is common in warm environments and can appear as small, red bumps or blisters on the skin, often on the torso and back.

Meningococcemia: Although rare, this condition is life-threatening and can initially present with a rash. The rash can start as small, red spots that quickly turn into purple patches, and it's crucial to recognize and treat promptly.
Kawasaki Disease: This condition can present with a rash, fever, and other systemic symptoms. Early recognition is critical for effective treatment to prevent long-term cardiac complications.
Staphylococcal Scalded Skin Syndrome (SSSS): Caused by staphylococcal toxins, SSSS can present with a rash that progresses to widespread skin exfoliation. It's more common in infants and young children.

Incontinentia Pigmenti: A genetic disorder that can cause a rash in infancy, characterized by blistering, followed by wart-like growths, and eventually, swirly pigmentation.
Congenital Syphilis: Can present with a rash, among other systemic symptoms, in infants born to mothers with untreated syphilis.
Langerhans Cell Histiocytosis: A rare disorder that can cause skin rashes, among other symptoms like bone lesions and organ dysfunction, due to abnormal proliferation of Langerhans cells.