Yes, I agree, do not mix the medicines - it cannot be of benefit and might confuse the case.
If using homoeopathy, take the child to an excellent dependable homoeopath. This would be the best option, if you have access to such a practitioner in whom you have complete confidence. Such homoeopaths on whom one can depend in acute situations are rare, but do exist.
Otherwise, use allopathy alone for the acute - i would try antibiotics before steroids if allopathic medicine is what you have to choose.
all the best, anna