It is not common to develop a food allergy
at this age although not impossible. if the rashes he had developed were definitely after eating a specific food (which must happen every time) then a diagnosis of rash secondary to food allergy is plausible. What you describe is something like cholinergic urticaria, a form of urticaria (this is not allergy in >80% of cases) that is triggered by temperature changes and mast cell release of mediators like histamine. Scabies is also a possibility that is intensely itchy and needs to be excluded with a careful examination, skin scrapings or a course of treatment if there is high clinical suspicion.
Atarax is a strong antihistamine (sedative, so take at night) and prednisolone
must be stopped after 5 days giving atarax a chance to work. You can switch to non-sedative antihistamines like fexofenadine
or cetirizine. There is no blood test for a definitive diagnosis but thyroid disease
or diabetes need to be excluded along with a complete blood count
to ensure there is no infectious trigger.
Hope that helps.