Folliculitis: Given the context of a prison environment where hygiene and skin care might be challenging, and considering the presentation of red bumps, folliculitis is a common condition that could easily occur due to shaving, friction, or bacterial infection of the hair follicles.

Contact Dermatitis: This could be due to an allergic reaction or irritant reaction to something in the environment, such as laundry detergent, soap, or even bed bugs or lice, which are more common in crowded living conditions.
Scabies: A parasitic infection caused by the mite Sarcoptes scabiei, which is highly contagious and can spread quickly in close living quarters like prisons.
Insect Bites: Given the living conditions, insect bites from bed bugs, fleas, or mosquitoes could cause red bumps on the skin.

Methicillin-Resistant Staphylococcus aureus (MRSA) Infection: MRSA is a serious bacterial infection that can present as skin lesions and is particularly concerning in crowded environments like prisons where it can spread quickly. It requires prompt treatment to prevent serious complications.
Cellulitis: A bacterial skin infection that can cause redness, swelling, and warmth of the skin. It can become serious if not treated promptly.

Keratosis Pilaris: A condition characterized by small, rough, sandpapery bumps on the skin, often on the arms, but it's less likely given the acute presentation of "red bumps."
Pityriasis Rosea: A skin condition that can cause a rash, but it typically starts with a single "herald patch" followed by a wider rash, which might not fit perfectly with the description of red bumps on the arms.
Allergic Reaction to Medication: If the patient is on any medications, an allergic reaction could cause a skin rash, but this would be less common and more dependent on the specific medication and patient history.