OP - I can hear the desperation in your typing - I'm so sorry this is happening to you.
Unfortunately, even if you got him a CAMHS assessment, or the GP agreed to do something, or someone else offered some assistance, it sounds like you are going to struggle to get him to engage if he's got to attend somewhere.
Will he even attend a GP appointment with you for example?
I'm sorry to say that the only way he's going to get any attention where he has literally no choice but to engage will be with police involvement. Whether that's as a result of you calling them, or him falling in with the wrong people and getting wrapped up in something else he shouldn't.
I agree with the posters who say that you need to call the police each and every time he turns violent.
Here's s20 of the Children Act that @Startinganew32 mentioned - https://www.legislation.gov.uk/ukpga/1989/41/section/20
There are safeguarding concerns for your other children too in all this.
https://www.fostercareuk.co.uk/knowledge-centre/reasons-for-a-child-to-be-taken-into-care - there's a section on this page about "voluntarily putting a child into care" that says:
"On some occasions, parents may place their child into foster care voluntarily... voluntarily placing a child into foster care mainly occurs when parents cannot, or do not want to, care for the child any longer.
It should also be noted that children may need to be put into care due to their own actions, if their parents cannot take care of them or manage their behaviour anymore."
I know it's not a decision that any parent would take lightly, but you have a duty of care to your other children also and none of you should be living in fear in your own home.