"Appointment prioritisation for vaccine"

I am exclusively breastfeeding a newborn so I expected to have my vaccine at the time I'd booked the appointment for (I timed my baby's feeds and child care around it). Arrived and there was a line, I believe, 140 people long. Was able to skip most of the line but was still late and my baby had been screaming for a feed by the time I got home to them. In my opinion, I would expect that exclusively breastfeeding women would be prioritised and would be able to attend their appointment at the booked time.