Viral Exanthem: This is a common condition in children, characterized by a rash that appears in conjunction with a viral infection. The history of previous fevers and the current presentation of a rash on the upper back and upper chest are consistent with a viral exanthem, which could be caused by various viruses such as roseola, measles, or enteroviruses. The age of the child and the nature of the symptoms make this a plausible diagnosis.

Roseola: Specifically, roseola infantum, caused by human herpesvirus 6 (HHV-6) or human herpesvirus 7 (HHV-7), is a common illness in young children that starts with a high fever followed by a rash once the fever resolves. The rash typically appears on the trunk.
Measles: Although less common in areas with high vaccination rates, measles can present with fever, followed by a rash that starts on the face and spreads to other parts of the body, including the upper back and chest.
Scarlet Fever: Caused by Group A beta-hemolytic streptococci, this condition presents with a rash that feels like sandpaper, fever, and other symptoms like a strawberry tongue. The rash can appear on the chest and back.

Meningococcemia: This is a severe infection caused by Neisseria meningitidis that can present with fever and a rash. The rash can be petechial or purpuric and is a medical emergency. Early recognition and treatment are crucial to prevent severe outcomes.
Kawasaki Disease: An acute febrile illness of childhood that can lead to coronary artery aneurysms if not treated promptly. It is characterized by fever, rash, conjunctivitis, cervical lymphadenopathy, and changes to the lips and oral cavity.
Staphylococcal Scalded Skin Syndrome (SSSS): Caused by staphylococcal toxins, SSSS presents with fever, rash, and skin exfoliation, primarily in infants and young children.

Juvenile Idiopathic Arthritis (JIA): Some forms of JIA can present with fever and rash, although this is less common. The systemic form of JIA is more likely to have such a presentation.
Infectious Mononucleosis: Caused by Epstein-Barr virus (EBV), it can present with fever and rash, especially if the child is taking ampicillin or other penicillins.
Erythema Multiforme: An immune-mediated condition that can be triggered by infections or medications, characterized by a distinctive target-like rash. It is less common in young children but should be considered in the differential diagnosis of a child with fever and rash.