It is hard to tell what the white heads on the palms and feet are without seeing them. However, given the data you provided (water works infection with heat rush that is worse now), your boy might have acquired another infection or the infection was presented on the palms and feet with pus collection in the canals of the skin glands.
You might want to take your boy to a pediatrician or a dermatologist where a physical examination will follow. If bacterial infection is detected as the cause for the whiteheads, then antibiotics might be recommended.
Meanwhile, keep the affected areas clean, because they might affect the connective tissue beneath the skin which is considered an additional complication. If the white heads burst and pus comes out, then a swab might be taken for a culture to detect the bacteria and the most effective antibiotic.
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