You are correct in assuming that the row was a domestic incident and as a dc (do you only have one?) was present the police are obliged to notify SS who will most probably be in contact with you at some point in the next week or so.
But please don't panic as this doesn't mean your dc will be found to be at risk and the act of reporting your h for drinking and driving doesn't mean that he'll be apprehended unless the police spot the car while he's at the wheel and he's found to be over the limit.
Making the call was absolutely the right thing to do and the only thing you could do as your drunken h presents a risk to other road users, including pedstrians, as well as to himself and, as Asprilla has said, you'd never forgive yourself if anything untoward occurred and you hadn't done your utmost to prevent it.
Do you have any idea where your h may have gone? Is there a handsfree mobile device in the car? If so, you may wish to call him and tell him to get off the road, park up in a side street, and find an all night cafe/fast food shop where he can get a coffee before crashing out for a few hours on the back seat of the car or, providing you feel able to face him, getting a cab home.
The night magnifies negative events and makes them seem far worse than are when seen in the clear light of day. You've demonstrated that you're a woman of courage and i have no doubt that you'll be more than able to meet any challenges that may arise from your h's crass stupidity.
Try to get some sleep or at least lie on a bed or sofa, close your eyes, and visualise a scene that's particularly pleasing to you - it might be a work of art, a tropical beach, or your dc laughing up at you. Lose yourself in the scene; experience all the feelings you'd have if it was taking placing now and let all other thoughts wait their turn until you're able to tolerate their intrusion.
It will all work out as it's meant to do and you must NEVER EVER reproach yourself, or allow your h or anyone else to reproach you, for doing the right thing.