Have you responded to the request for driver's details yet? You received it more than two months ago and had 28 days to reply. When you last posted before today (in May) you seemed to have little idea of who was driving and no recollection of the occasion. If you haven't responded by now I imagine the police might be in the process of prosecuting you for failing to do so.
Everything you have mentioned actually aggravates the offence (i.e. makes it worse). If you have disabilities which affect your driving you should declare them to the DVLA. If, as you suggest, you are unable to apply the brakes quickly in the event of an emergency (such as when you see a speed camera whilst you are exceeding the speed limit or when a child runs out from behind a parked car) they may ask for a medical report and, as above, perhaps decide they will not allow you to drive.
If you responded in time naming yourself as the driver you should have received the offer of a course by now. If you haven't you should contact the police asap and try to persuade them not to prosecute you for failing to do so.