Hand, Foot, and Mouth Disease (HFMD): This is the most likely diagnosis given the symptoms of rash on hands, feet, and mouth, especially in a 12-year-old male. HFMD is a common viral illness in children, typically caused by coxsackievirus A or enterovirus 71, characterized by these specific symptoms.

Erythema Multiforme: This condition is characterized by target lesions on the skin and can also involve the mucous membranes, including the mouth. It can be triggered by infections or medications.
Kawasaki Disease: Although more common in younger children, Kawasaki disease can present with rash, fever, and oral changes, including redness of the mouth and throat.
Impetigo: A bacterial skin infection that can cause sores or blisters on the hands and feet, and can also involve the mouth area if scratched and infected.

Stevens-Johnson Syndrome (SJS) / Toxic Epidermal Necrolysis (TEN): These are severe skin and mucous membrane disorders, usually a reaction to medication or infection. They can present with skin lesions and mucous membrane involvement, similar to the described symptoms, but are much more severe and potentially life-threatening.
Meningococcemia: A severe infection caused by Neisseria meningitidis, which can present with a rash, but is distinguished by its rapid progression and severity, including potential for sepsis and meningitis.

Pemphigus Vulgaris: An autoimmune disease causing blistering of the skin and mucous membranes, which could potentially present with oral lesions and skin rash.
Paraneoplastic Pemphigus: A rare autoimmune disorder associated with underlying neoplasia, characterized by severe mucosal lesions and skin blistering.
Enteroviral Exanthem (other than HFMD): Other enteroviruses can cause rashes and systemic illnesses, though the specific pattern of hand, foot, and mouth involvement is more characteristic of HFMD.