Absolutely appeal OP. The cost or not to schools, LAs or academies is not your concern. You did not create this system, you just have to try your best to navigate it.
Firstly make sure you accept the offer you have. This won't change the outcome of any appeals or wait list places but if you don't accept, the LA won't be obliged to find you another place. You'll have to do that yourself.
Then get yourself onto the waiting lists for the schools you want. Some LAs do this automatically for your higher preference schools others don't. Also check to make sure they have you in the correct category on that waiting list eg catchment, distance etc
Also check that admissions have the correct address for you. Getting a digit wrong on your street address could make a difference if the last admitted distance is very close.
Look at advice on here about appealing places. You need to show that the school you want has things that will benefit your daughter. So not how terrible the other school is but specific things the school you want does do that would benefit your child.
If the school you want is over subscribed then you need to show that the detriment to your daughter of not attending is greater than the detriment to the school of having an extra pupil.
Generally transportation issues aren't considered (having to catch multiples buses etc) but it won't hurt to explain that because of your daughter's additional needs she could/will find this much harder or impossible.
Good luck