Sending lots of love. There will be lots of 'Just do-' but it's so complex and almost impossible balancing other responsibilities and the needs of your other children who don't just stop existing.
Sister wasn't outwardly aggressive, she turned inward and it was school refusal, totally withdrawing, self harm, suicidal ideation. My and my brother had nothing close to that. If your other kids are generally coping and normally behaved and there was no additional trauma for your youngest (death in the family etc) then probably not your parenting but an underlying cause.
In our case after decades of going through mental health issues we found out she has a dramatic hormone imbalance and has been on HRT for years to correct this. She's working through the trauma that those years did to her but she's a different person.
Connect with your husband. You have to approach this as a team and have clear and consistent approach. Honestly I'd use the limited funds on counselling for yourselves to get a game plan together of how you will approach.
Get DS into any club. Martial arts, team sports and drama all have incredible impact on mental health. Diet genuinely also can have the moat transformative impact.
With the school and services, they are so under-resourced, it will be a battle to get anything. Be the squeaky wheel, follow up again and again and again. Everything in writing and lay it out, "We have requested early intervention for escalating aggression that has lead to violent outbursts against me and my other children. Based on this pattern we expect violent incidents to increase jeopardising the welfare of other minors. Can you confirm that despite this danger you are unable or unwilling to refer to..." Never play anything down, keep pushing.
Good luck.