Most Helpful Girl
Reading this, I estimate you will. What you will need to do is document that you are tending to the child. Meaning, get any records of the doctors' appointments and take pics of you taking care of here etc. You also should find a way of documenting his behaviour, if possible. Then you can make it a custody case, and have increased the likeliness of you winning.
You also have the advantage of being a woman here, since often it is decided a child should remain with its mother, especially in america. Strange question, but are you breastfeeding? Because that would also help, seeing as you would be the only one able to feed the child without it having to adapt to bottle feeding.
I wish you good luck and I am sorry you have to go through this.