Insect Bite Reaction: This is a common condition in children, characterized by an initial itchy spot that can progress to a bullous lesion and eventually become a solid papule. The history of the lesion starting as an itchy spot and evolving is consistent with an insect bite reaction.

Eczema (Atopic Dermatitis): While eczema typically presents with multiple lesions and is associated with other atopic diseases, it can sometimes manifest as a single, large, raised papule, especially if scratched. The initial itchy phase could be consistent with eczema.
Keratosis Pilaris: This condition causes small, rough papules, but in some cases, especially if scratched or irritated, these papules can become larger and more inflamed, potentially resembling the described lesion.
Molluscum Contagiosum: A viral infection that causes small, pearly, or flesh-colored bumps. The lesions can become inflamed and larger if scratched, which might fit the description given.

Cellulitis: Although less likely given the description of a single, solid papule, cellulitis is an infection of the skin and subcutaneous tissues that can present with redness, swelling, and warmth. It requires prompt antibiotic treatment to prevent serious complications.
Mastocytoma: A rare tumor that can cause a solitary lesion. While uncommon, it's a condition that shouldn't be missed due to its potential implications, including systemic mastocytosis in some cases.

Xanthoma: These are rare, benign growths composed of fat-laden cells. They can appear as yellowish papules or nodules and, although uncommon, could be considered in the differential diagnosis of a child with a solitary, raised skin lesion.
Langerhans Cell Histiocytosis (LCH): A rare disorder in which the body accumulates too many immature Langerhans cells, part of the immune system. Skin lesions can be part of the presentation, although LCH is more commonly associated with systemic symptoms and other organ involvement.