It sounds like you will be very near the top of the waiting list. Can you find out more about movement in the school and how likely it will be that you might get a place?
There will be more knowledgeable people along soon, with a lot of very good advice for you. Can you say more about what the admissions policy is for the school - what are the criteria? Is it based on children in care/SEN, then siblings, then church attendance, then proximity for example? Did you meet all the religious requirements?
What does the school say about admissions on medical need?
You would need to get a lot of documentation, including letters from the doctor, to show that this school would adversely affect your daughter. But what you actually need to show is that this school will meet those medical needs. As I understand it, the local authority could offer you another school, where there is no building work.
It is always worth appealing if only so you know that you have done everything you can. But if it is an infant class size (ICS) case then you will only succeed if you can show that a mistake was made that cost your child a place. For example, if the religious attendance wasn't read correctly, so your child didn't get in, but a child from a further distance did get in. It doesn't sound like this was the case for you though?
Another tactic some people are trying, where they are waiting for a space at a school that has a history of movement, is to defer starting. If your child was born after December, you could possibly hold of them starting in reception. It could be that a place comes up while you are waiting.