I am so sorry, this must be so hard.
Please put your energies into getting more help for you and long term support for him.
Please see if you can get some counselling which will help you to manage your own feelings and cope better.
Would a residential centre be better for him?
I am so sorry this must have been really hard to write and not know how it would be received. Sometimes I am angry and feel upset with my kids and they are much, much easier than your son appears to be.
I think that you need specialist help and it may be that Theraplay' (a special kind of play therapy) could help to build a better bond between you and your son and also help to calm him.
My son is 7, adopted, and has had some real explosive episodes and theraplay made things a lot better. It may or may not work for your son but this is the sort of help you could ask for.
If you are really fobbed off I would engage your local MP and get them on side and helping you.
I would call and email any part of the local authority that can help you and be nice, persistent and desperate. Not aggressive to piss them off but sufficiently persistent that they feel they will give you want you need to shut you up a bit.
Make lots of notes of what you need, what may help and what may be available. In the middle of all that mess of word will be something that may work.
If he needs to go to school out of area, could this be funded, and his bus journey too etc on school transport and could this give you more time to recuperate and recover?
I think you need to phrase it always as 'my son needs' my son deserves (an education/help etc) but also always be looking for what will work for you and make you better able to cope, to care and survive.
You need to show the local authority how much your son needs help while realising anything they offer that helps him, gives you time, offers hope etc, will help you.
We got help with our son and daughter (birth dd, more trouble than ds!) last year because I cried down the phone. I didn't mean to, it wasn't a trick, I had just reached the end of my tether. I am guessing for you that the end of your tether is a distant memory.
But now, you know you can do this, please think of yourself, but ask always for things that will work for your family, you and your son.
Someone once wrote... something like....I like to think that every story has a happy ending, if you are not happy, this is not the end.