You need to apply to your new LA. They must come up with a place for your son somewhere.
If the place offered is not at your local school you can appeal but most Reception appeals are infant class size cases, which are almost impossible to win unless there has been a mistake in the admissions process that cost your son a place.
You won't get priority based on the fact your son has no place. However, if the LA isn't able to come up with a place for him within a reasonable distance, he can be admitted to a local school even if that takes the school over the infant class size limit. If they fail to do so, that would potentially be grounds for appeal.
Proximity will give you priority on the waiting list and is likely to put your son at the head of the list, but it won't guarantee a place.
Contrary to what most posters have said, your disability may also give your son priority. Some schools have a "special medical/social needs" category or similar in their admission criteria. Whilst most limit this to the child's needs, some include parental needs. But again, even if this does give priority, that simply moves you up the waiting list. It doesn't get you a place.
When the LA offers your son a place, you should accept it wherever it is. If you don't, they don't have to come up with any alternatives. However, given your son's age, if it isn't a school you want, you have the option of deferring entry to later in the school year (but no later than the start of the summer term next year) and hoping that a waiting list place comes up.
Alternatively, you can ask the LA about delaying entry for a full year. They have the final say on this, but I would expect them to agree. You can then apply this autumn for places to start next September. Given your location, you would almost certainly get a place at the local school.