Degreechick,
I don't know who you have been talking to but they are giving you bad advice.
Firstly you should have been able to change your admission preferences upto and including the last day, that is 12th december. In fact every LA's information will go into great detail confirming that you must do this or you could loose the place if you do not tell them about address changes. You should also have been given some priority to do this given the sensitive situation you were in.
I am guessing that you have no letter or email from the LA over this, it was all over the phone.
Accepting that the school preferences did not get changed, it is not a great surprise that you have been allocated a school that was one of your preferences. But the advice you have subsequently been given is totally incorrect. Firstly by law your child has to start school in the term after their 5th birthday, so when is their birthday? I don't see that starting a year later is appropriate as you have been allocated a place this year and the school cannot keep that place reserved for you for a year.
You can appeal for any school you wish to, which you believe is safe for your child. You do this by asking the local authority for a place at the school. If there is a space then the LA has to give it you, if the school is full then you can appeal for a place. You are going to run into issues of schools that have appeals that are based on the infant class size regs, that is no more than 30 in the class,unless you have documentary proof that you tried to change the preferences before the 12th Dec and you were refused. If you have that in writing that will make things a lot easier to win at an admission appeal.
Please do not feel that you are on your own here, you should be getting help from other services and they should be making efforts to get your child into a school so that a level of stabilisation can occur.