Insect Bite Allergy or Contact Dermatitis: The rash's appearance on exposed areas like the tops of forearms and face, especially after being outside in the mountains, suggests an allergic reaction to insect bites or contact with certain plants. The fact that the rash resembles hives and came and went supports this diagnosis.

Sunscreen or Insect Repellent Allergic Reaction: Despite the denial of sunscreen use, it's possible that some form of sunscreen or insect repellent was applied, causing an allergic reaction. The pattern of exposure and the description of the rash could fit this scenario.
Erythema Multiforme: This condition can be triggered by various factors, including viral infections or allergic reactions. The rash's appearance and the fact that it came and went could be consistent with erythema multiforme, although it's less common in this context.
Atopic Dermatitis (Eczema) Flare: While less likely given the acute onset and resolution, an eczema flare triggered by environmental factors (like dry mountain air or exposure to allergens) could present similarly.

Urticaria due to Anaphylaxis: Although the child's symptoms seem localized and not immediately life-threatening, urticaria can be a sign of anaphylaxis, especially if there's a history of allergy. It's crucial to assess for other signs of anaphylaxis, such as respiratory distress or cardiovascular instability.
Lyme Disease or Other Tick-Borne Illnesses: Given the outdoor exposure in an area potentially endemic for tick-borne diseases, it's essential to consider these diagnoses, especially if the rash does not fully resolve or is accompanied by systemic symptoms like fever.

Phototoxicity due to Plant Exposure: Certain plants can cause phototoxic reactions upon exposure to sunlight, leading to rash and blistering. This would be less common but could be considered given the outdoor exposure.
Autoimmune Conditions (e.g., Juvenile Dermatomyositis): These conditions are rare in young children but can present with skin manifestations, including rash and photosensitivity. They would be considered if the rash persists, worsens, or is accompanied by other systemic symptoms.