Contact Dermatitis: This is a common condition that occurs when the skin comes into contact with an irritant or allergen, leading to a rash. Given the sudden onset and location of the rash on the arms and chest, it's plausible that the patient came into contact with something that triggered the reaction.

Allergic Reaction: An allergic reaction to a medication, food, or environmental factor could cause a rash on the arms and chest. The lack of response to over-the-counter medication might suggest an allergic component.
Eczema (Atopic Dermatitis): Eczema is a chronic condition that can cause itchy, inflamed skin. While it often starts in childhood, it can persist into adulthood or even begin in adulthood, making it a possible diagnosis for this patient.
Viral Exanthem: Viral infections can cause rashes, and given the acute onset, a viral exanthem (such as from a viral infection like measles, though less common in adults due to vaccination) could be considered.

Stevens-Johnson Syndrome (SJS) / Toxic Epidermal Necrolysis (TEN): Although rare, these are life-threatening conditions usually triggered by medications or infections. They can start with a rash and progress to widespread skin necrosis and detachment. Early recognition is crucial for survival.
Lyme Disease: If the patient has been exposed to ticks, Lyme disease could be a consideration, especially if the rash has a characteristic "bull's-eye" appearance.
Meningococcemia: This is a severe infection caused by Neisseria meningitidis, which can present with a rash. It's critical to identify and treat promptly due to its high mortality rate.

Pityriasis Rosea: A condition characterized by a rash that typically starts with a single, large spot (herald patch) followed by smaller spots, often on the trunk and limbs. It's usually self-limiting but can be uncomfortable.
Kawasaki Disease: Although more common in children, Kawasaki disease can occur in adults and presents with fever, rash, and other systemic symptoms. It's a rare but important diagnosis due to its potential for cardiac complications.
Syphilis: The secondary stage of syphilis can cause a rash on the palms and soles, among other places. Given its potential for serious complications if untreated, it should be considered in the differential diagnosis, especially if other risk factors are present.