If the appeal is for a place in Y3 you have to show that the prejudice to your child outweighs the prejudice to the school, not just the other 30 classmates. You can also win if you can show that a mistake has been made and your child should have been offered a place - that would be a stronger case than relying on prejudice. If it is for Reception, Y1 or Y2 this will be an infant class size case which means you can only win if you can show that a mistake was made.
Net capacity assessments don't apply to academies. Their capacity is determined by agreement with the DfE. It is therefore possible that the information you have been sent is old, possibly from before they became an academy.
If the school gives priority based on medical needs you may be able to argue that a mistake has been made. This will only work if the medical evidence is clear that the medical professionals are giving their opinion, not simply repeating your view, and the medical evidence shows that your child needs to go to this particular school. Your child does not get priority for simply having a medical condition. It needs to be something that means the school you want is the only appropriate school, e.g. a child being wheelchair bound needing a place at the only school in the area that is fully wheelchair accessible.
If the school doesn't prioritise on medical grounds you can still use your medical evidence to argue that your child will be disadvantaged if not admitted to this school provided their condition means this is the only appropriate school.
You should also look at things the school provides that are not available at the offered school. If there is anything that is particularly relevant to your child that is worth bringing up at appeal.
Note that you should still make a prejudice case even if you think a mistake has been made. If several children have been affected by mistakes the appeal panel may decide they can't admit all of them, in which case they will have to decide which of the children are most in need of places at this school.
You will receive a copy of the school's case before the hearing. Look for any weaknesses you can use. You will be given a chance to question the school's representative after they have presented the school's case. That is a good time to bring up any weaknesses you have spotted. If you need help with that post an outline of the school's case here and you will receive some advice.