Sorry about this illness. You have not mentioned how anemic he is, i.e. the hemoglobin level. If moderate to severe, that may be the cause or else if mild only, that may be due to repeated infections. Allergy does not have much fever usually.
He needs to be investigated for genetic or other causes of low immunity so please consult an immunologist or infectious disease specialist for needed work-up.
Meanwhile please get a prescription for prophylactic antibiotic course for few weeks, like trimethoprim.