"Not allowed to see a doctor"

I called my GP surgery to ask for an appointment for my feverish baby.

Over the phone the person in reception said they were very busy and there was no appointments, so they advised to go to the surgery and hopefully a nurse will see him.

When I arrived to the surgery another person in reception was taking note of patients who had appointments today and telling them they will reschedule their appointments. They were very rude with the gentleman in front of me and speaking loudly so everyone can know his reason of attendance which I consider a lack of privacy. They were saying that the NHS send them a note to not to switch on the computers and they were unable to see any patients unless you are practically dying, and apparently my baby is well enough to wait until God knows when they will work again.

In the waiting area there was another lady with a toddler awaiting to be seen by the doctor.

Is my 10 months baby who is been vomiting with fever and an ear infection not sick enough to see a doctor?

I don't understand the criteria and how a receptionist can deny your right to see a doctor and let other do it without medical training.