Between the behaviour issues and screaming during nap time, I'd let him go. All children need to feel emotionally and physically safe in your care, whether it be your child or someone else's. If you need to "shadow" a child like that to prevent issues, that has now become 1-1 care, and that's not feasible in our business. I would have terminated on the spot, with a phone call to parents to do an early pickup, and be gone. Biting can be normal in toddlers, especially in speech delays, but drawing blood over a sharing issue elevates it to a whole different level. I would have emailed the parents a pic of my child's bloody face. Keep a picture of the injury for your own sake. It wouldn't be the first time an angry parent calls CAS because they were terminated!
Do you write up detailed accident reports when an injury happens? I always do if it leaves a mark, or is a frequently occurring aggressive behaviour, and then I get the parents to sign it. Cover your butt on this one! Zero tolerance here for incidents that draw blood intentionally.