Hit a woman this morning and got a fine

Do not pay the fine.
Elect to go to court.
(If it goes to court, which isn't likely)
Put on a suit.
Explain to the Magistrate truthfully what happened.
Yes you shouted for which you apologise, but you had been under stress as you had feared for your life and hers as the traffic bared down upon you both.

That is what I would do personally.
coming from the man, who's spent a night in the clink for riding dangerously and trying to outrun the police. ha!