Fever and fatigue, followed by itchy mosquito-like bumps on hands that spread? allergies?

Fever: No. Fever is not a manifestations of allergies unless a complication arises.

Infection: Viral or streptococcal. You should have a rapid step or throat culture to rule-out streptococcal throat infection. If negative you have a viral infection that requires only rest and supportive care. The photo shows a child with scarlet fever, a rash associated with streptococcal infection.