I read your post again and suddenly realised I was in a very similar situation once.
I was 17 years old not long passed my test and driving a Hillman Imp on my way to college. (This was in 1983)
I was in the outside lane of a dual carriageway approching a set of traffic lights. They had just changed to green so I maintained a steady speed.
Next thing was a car suddenly pulled out of the inside lane straight out in front of me causing me to do an emergency stop. The brakes on a Hillman Imp were rubbish, but as I was skidding there was a side junction to the right so instead of ploughing into the back of the car that had pulled out infront of me I started aiming for the junction. Unfortunately I overshot the junction and hit the bollard on the central reservation causing me to spin around. I remember the bang when my right side rear wheel hit the curb of the central reservation.
At this point I was in a bit of shock, car was bent and didn't know who to have a go at because I didn't know who it was that pulled out on me.
A guy came over asking if I was ok, he said he saw what happened and gave me his details. At first I thought it was him that caused me to crash, and I kept thinking who the hell was it that pulled out on me?
I went to my insurance, told them what I knew that happened and the name and address of the guy that I spoke to, although I still didn't really know who he was.
Sometime later, may have been 6 - 12 months I had a strange looking letter through the door, not like I seen before. It was from the law courts in Birmingham basically telling me that the woman of the vehicle involved im my incident had been found guilty of careless driving and I recall I had compensation of £300.
The funny thing was I remember thinking, I don't rembember seeing anyone apart from the guy, no ambulance or police arrived at the scene, I certainly don't remember seeing a woman. My conclusion was she must have drove off.
I am grateful for the guy who stopped by as a witness.
Get as much info as you can and witnesses. Call for an ambulance to get you checked over. You might feel ok at the time but might suffer later. Get the police involved.
And let the insurance sort it out, it might take time but you never know.
Hope you get back on the road soon