Not at fault & 3rd party insurance

Coming home from work last Friday a car cut in front of me
. Long story short I hit it, police and ambulance arrived, and the lady got fined for not giving way. I spent 1hr in the hospital so all is good.
Now I only have 3rd party insurance. So I suppose I need to get 2 quotes to give to the lady for her to claim insurance?
I haven't told my insurance anything as I was not at fault.
Is this the correct assumption?
And what if the damage is to the frame/fork (as I hit it head on).... how will "write off" be determined?

Now I only have 3rd party insurance. So I suppose I need to get 2 quotes to give to the lady for her to claim insurance?
I haven't told my insurance anything as I was not at fault.
Is this the correct assumption?
And what if the damage is to the frame/fork (as I hit it head on).... how will "write off" be determined?