I am an experienced driver and rarely get into difficulty, but actually I did something a bit like this once a couple of years back, when I was about to get up to the school.
A white van man came up and shouted at me and was pretty angry. It transpired that my wing mirror had clipped his but I had been completely unaware. I had an ear infection at the time so hadn't heard a noise. Anyway, I just held my hands up and said I was really sorry, totally unaware as I have a hearing impairment at the moment, asked what actually happened, asked where did it happen, and asked if I could help him find his wing mirror. I then gave him my name and address and said if you need a new wing mirror I must cover the cost of that.
In the event we found it on the road and it just needed popping back in, although it had a slight crack. Once he realised I hadn't driven off on purpose (which is a criminal offence and called a Fail To Stop) he was fine and very reasonable. I never heard anything from him so I think it wasn't worth him pursuing really - you can buy new ones very cheaply if you know where to get them, and I imagine that's what he did.
So generally better to hold up your hands to any damage. I would mention to the police that you noticed your wing mirror was clipped and you are worried this might have been you doing it to someone else as you are a new driver. leave your registration number and name and address and I imagine you may never hear anything about it. But the fact you have confessed properly before the other person has raised it will prevent any criminality problems.
And the big moral of the story is that there is no excuse for a fail to stop other than it would put you in physical danger (e.g. personal safety at night in a dodgy area, extreme weather conditions). The school run is really not a proper excuse for anything really 