Irritant Contact Dermatitis: This is the most likely diagnosis due to the common exposure of hands to various irritants such as soaps, detergents, or other household chemicals, which can cause skin irritation in toddlers who often explore their environment through touch and mouthing.

Allergic Contact Dermatitis: Possible if the child has been exposed to allergens like nickel, certain plants, or specific ingredients in soaps or lotions, leading to an allergic reaction.
Atopic Dermatitis (Eczema): Given the age, atopic dermatitis is a common condition in toddlers, characterized by itchy, inflamed skin, which could manifest on the hands.
Infection (Bacterial or Fungal): Infections such as impetigo or fungal infections like ringworm can cause hand irritation and are relatively common in children.

Scalds or Burns: Although not an infection or dermatitis, it's crucial to consider burns or scalds as a cause of hand irritation, as they require immediate and specific treatment to prevent further injury.
Child Abuse: In cases of unexplained or recurrent hand injuries, child abuse must be considered and investigated appropriately.

Kawasaki Disease: A rare condition that can cause skin peeling and irritation, among other symptoms, but is typically accompanied by fever, rash, and other systemic signs.
Staphylococcal Scalded Skin Syndrome (SSSS): A rare but serious condition caused by staphylococcal toxins that can lead to widespread skin irritation and peeling, often starting around the face and spreading.
Erythema Multiforme: A skin condition characterized by target lesions, which can be triggered by infections or medications, and although rare, it can cause significant discomfort and requires specific management.