I would report it, even if its just to 101 so that its logged - just in case - then at least its on record.
Why would SS be involved? I reported my DH after he flipped the sofa over with me on it when he was in a drunken rage, gave statement and he was cautioned but not charged, as far as I am aware SS was not informed.
Hand holding until someone more knowledgeable comes along
You need to report this, choking you places you as high risk of further and escalating violence. At the very least you need to see the dr and have it logged there because it can cause serious damage that may not show initially. Its actually very easy to go too far and kill someone like that when meaning to "just" hurt or frighten them. Please think about that, because you very easily couldnt have been able to go to your daughter tonight. He could have killed you. Please, please, as a bare minimum, get information on creating a safety plan and a plan on how to leave, even if you dont currently plan on using it now. It could save your life one day. If you are in the NE i can direct you to the domestic violence advoates i use, they can offer support and info, if not, womens aid can help.
Where you go now is straight to the phone and call the police because your h has physically assaulted you and if you don't report this incident, he'll do it - again and all the pictures in the world of red marks on necks won't stop him including the one you've taken of your own.
You need have no fear of SS involvement as you haven't committed any crime and by reporting him you will have demonstrated that you can protect your dd from any (further) distress/trauma she may suffer from seeing/hearing her df attack her dm.
You can visit the womens aid website now OP. You can use the incognito browser on your phone so your partner wont be able to see you visited it. Please consider the police though. Violence of this sort is never a one off and it usually escalates after the first incidence of violence. Theres not much worse it can get after choking, and your daughters deserve their mum to be alive, healthy and happy. Im worried for you OP, you can PM me. Im here.
Tell him to leave right away, arm yourself with something if need be. Call the police in the morning. How dare he do that to you?! What if he hadn't stopped and your kids are in the house with him???! Nah. He has to go.
Yes, call the police. I didn't, when my then-husband tried to strangle me to death, but that was 1986 and women are more likely to be listened to today. Please do it. If he can choke people, he has it in him to kill them.