Contact Dermatitis: This is a common condition that occurs when the skin comes into contact with an irritant or allergen, causing redness, itching, and small bumps. Given that the patches are on the arms and spreading, it's plausible that the individual has come into contact with something that's causing an allergic reaction or irritation, which could be from a variety of sources such as metals (like nickel), certain fabrics, dyes, or even soaps.

Eczema (Atopic Dermatitis): Characterized by itchy, inflamed skin, eczema can appear anywhere on the body and can spread. It's a chronic condition that may be triggered by allergens or irritants.
Psoriasis: An autoimmune condition that speeds up the life cycle of skin cells, causing cells to build up rapidly on the surface of the skin. The extra skin cells form scales and red patches that itch or burn.
Seborrheic Dermatitis: A condition causing scaly patches, red skin, and stubborn dandruff. It often affects oily areas of the body, like the face, but can also appear on the arms.

Cellulitis: A bacterial skin infection that can cause redness, swelling, and warmth of the skin. It can spread rapidly and, if not treated promptly, can lead to serious complications.
Lyme Disease: Caused by a tick bite, Lyme disease can initially present with a distinctive "bull's-eye" rash, but it can also cause more generalized rashes or red patches on the skin.
Staphylococcal Scalded Skin Syndrome (SSSS): A condition caused by staphylococcal toxins that typically affects infants and young children but can also occur in adults with significant comorbidities. It causes widespread blistering and peeling of the skin, starting with red patches.

Pityriasis Rubra Pilaris (PRP): A rare skin disorder that causes constant inflammation and scaling (exfoliation) of the skin. It can start with small, rough patches on the skin and progress to more widespread involvement.
Kawasaki Disease: An acute febrile illness of childhood characterized by vasculitis of medium and small-sized arteries, particularly the coronary arteries. It can present with a rash, among other symptoms like fever, lymphadenopathy, and changes to the mouth and hands.
Erythema Multiforme: An immune-mediated disorder that can cause target lesions (red patches with a pale center) and is often associated with infections or medications. It can be a sign of a more serious underlying condition.