Were you speeding?
To be honest, I would take the fixed penalty.
A court still has to levy points event if it finds that there was mitigation. All that would happen is that you would end up with 3 points at court and a much higher financial penalty.
There is a defence of necessity to road traffic offences and duress to all offences but this doesn't get over it. It is a very difficult defence to run at the best of times. Come what may, your account explains why you did what you did but it would just plain be wrong to say that there weren't other options which is what necessity requires.
I'm very sorry but that is a reality I'm afraid.
Can I clarify anything for you?
All the best.