"trying to secure a GP appointment"

My daughter has been catching regular colds for the past few months, at the last GP visit she was given an inhaler and advised there is a possibility she could have asthma. This week has been particularly bad, I have been trying - between myself and her dad - since Wednesday to secure her a GP appointment, in addition she has missed a whole week of school. I eventually got through to the GP at late afternoon, after 42 attempts today alone, I was told no appointments available; I’m not unreasonable, I accepted this and requested an appointment for Monday or Tuesday. I was told these appointments were locked and I would be required to contact the GP again on Monday. I voiced my exasperation over this, given I have been consistently trying to get in contact with the surgery since Wednesday. I then frustratingly added I believed my sick daughter was being denied a service and I would have to consider using doctors on call as she was clinically not improving and I was not going to allow her to deteriorate for another week; the response to this was that would probably be your best bet. In this current climate, I find this appalling and unacceptable. Essentially, this weekend I am going to have to use urgent care services because I cannot be given a GP appointment for an increasingly poorly child.