This always happens with our GP too, it can be a nightmare. I ask them to see if they can squeeze us in if someone cancels and they sometimes can manage that on the same day.
if not, I ask if my doctor can ring me if I am very sick or if its one of my children who is quite sick and they usually manage the phonecall. If the doctor decides based on the phonecall that we are in need of attention, they will make sure we get an appointment that day.
Same with our gp – huge practice and lots of doctors but very hard to get an appointment. In saying that, kids tend to get sick out of hours – so more often than not, it will be the Doctor on Call. DOC is brilliant and in Navan, you are usually out within the half hour.