I can’t quite help on the treatment side of things (past basic first aid, monitoring his temperature, and so on, I don't know what other treatments might be offered!) but in terms of “general hospital procedures,” here are a few thoughts. The main book I refer to for questions relating to “what were hospitals like in the mid 20th c” is Sister Margaret Scales, Handbook For Ward Sisters (Bailliere, Tindall, and Cox, 1952). It’s a little later than your period, but one thing about nursing is that it remained stubbornly Victorian in its practices until the late 1950s.

If the parents bring the boy to the hospital, they might first walk in the front door and meet the hospital porter— responsible for transporting patients around the hospital, directions, etc. There’s always one at the entrance. The hospital might have a receiving department, where doctors or nurses briefly examined patients before admitting them, or a specific casualty department, which functions much as an emergency room. Any of these things will end with someone being admitted to a ward. It’s 1921, so the hospital may have a designated children’s ward— but it would have probably been pretty new. (On this point, I ran the phrase “new children’s ward” through the British Newspaper Archive and found way too many articles about hospital construction— in October 1927, the Hastings and St Leonards Observer announced the construction of a 20-bed children’s ward at the Royal East Sussex Hospital, fitted out with “a balcony all round and part open and part closed; and all the glazing will be with vita glass…. there will be the usual duty room, a small isolation room specially glazed, and medical officers’ rooms.”)

Paperwork: Not paperwork, exactly, but an interview with the ward sister, who runs the ward and everything that takes place in it (excluding the doctor who comes for rounds)— meals, bedtimes, visitors, ventilation, things patients have by their beds, patient observations, you name it. On being first admitted to the ward (or to the casualty department), a junior nurse will ask for the usual particulars— name, addresses, parents’ address, age. She’ll take the child’s temperature, pulse, and respiration rate, and record them in the ward logbook. Later on (ideally as soon as possible— but if the ward is busy there may be a wait) the ward sister will follow up with the parents (usually in her office, which is off the side of the ward)— perhaps getting more information about what happened, and telling the parents about procedures, visiting hours, and so on.

Would the family be allowed to see him? His parents would, if the boy is really ill. “Relatives of seriously ill patients often constitute a pathetic problem,” Scales says. “They need so much consideration and understanding, yet one seems incapable of giving it. Tea or a meal can always be offered in the ward and arrangements made for them to sleep the night in hospital.”

In general, though, sisters kept tight control over visiting hours. By the 1950s, according to Sister Scales, some sisters were allowing 30 min visiting periods every day, which was a change from the old model of 1 visiting hour per week. It’s plausible that children’s wards had exceptions to this— that parents of not-seriously-ill children could visit for 30 min or 1 hr every day. The reasoning? For Scales, “Too much visiting or too long a visit may be a tax on a patient, and that rest is essential if he is to progress. Unfortunately some relatives and friends fail to realize these things and do not understand that special times are set apart so that a whole ward may be quiet whilst patients rest.”

Hope this helps! Happy to answer (or at least take a stab at) any other questions on hospital procedures, nursing care, etc!