I don't imagine your mum wants to throw you out but there is only so much violence anyone can tolerate. First step is to consider if you can get help dealing with the ptsd and ways to divert the anger into other channels. Might sound odd but art therapy or cognitive behaviour therapy might be worth a try. Your mum might let you stay if there was a prospect of improvement. If she felt she had to have a break she might be able to let you return after therapy.
Social services should be your first point of call. If you are still under 16 do quickly as I believe they have some responsibilty up to 18 if you've seen them before 16.
You're unlikely to get a flat - b&b or hostel are more likely. Obviously the people there are likely to have problems, they may do drugs but drugs are not supposed to be in the accommodation. They will try to help you find work or some sort of training place. If you get a job you may be eligible for housing credit and tax credit, low paid workers get financial help too.
Sometimes churches do food banks, they normally only provide a few days foods and it can be mainly beans and prunes.