My dd also needs to use a wheelchair from time to time (Ehlers Danlos syndrome).
We started by visiting all the local secondaries to find out what they were like, in purely physical terms and in the feel of the place. It turned out there was only one local school which was wheelchair adapted.
Then we made an appointment to speak with the SENCO and head of Yr 7 at the school we thought would meet her needs. We explained about dd's situation and mentioned various situations that might cause her problems, and found them full of helpful suggestions. They obviously couldn't help with the actual application; this was more to confirm that they would be the right place.
We then applied for this school and adduced dd's medical needs ticking the box for special reasons. This is where we went slightly wrong as we did not provide enough professionally backed-up evidence of how dd's specific needs were matched by this school and this school only. So we were rejected and had to appeal. We won the appeal.
The evidence we won the appeal on (so what should have gone into the initial application) was:
dd needs to use a wheelchair from time to time (backed up by letter from GP and paed)- this is the only nearby school that is wheelchair adapted
however, she should walk as often as possible, and as her walking is not very good, she needs a small school(backed up by letter from GP and paed)- to avoid massive wheelchair adapted school
she needs frequent medical appointments and therefore has to be near surgery (letter from GP)- to avoid wheelchair adapted school at other end of LEA
she suffers from chronic pain issues which means she cannot travel long distances on a daily basis (supported by letter from paed and GP)- to avoid wheelchair adapted school at other end of LEA
she suffers from emotional health problems regarding her disability and needs to attend a school where her friends are going who can explain and help her make friends (backed up by letter from CAHMS)
On this we got in. We then applied to the LEA for transport and got it. However, because the distance was less than they would usually provide transport for, I had to provide medical evidence as to a) why she could not go on public transport (disability) and b) why I could not drive her myself (no driving licence due to poor eyesight)- the GP saw to that.