Your insurer should sort everything out financially .
Your good lady should go to the doc and get checked in case there is anything more than soft tissue damage ; if there is ongoing soreness beyond a day or two ( whiplash ) then you will need the doctors report anyway .
Before it is too late : witnesses , photos , cctv .
BTW , if the other party has admitted liability , speak directly to their insurer - sometimes they will settle directly with you , provide replacement car , deal with the claim themselves as it cuts out middle men and costs them ( and all of us ) less in the long run . You still have to inform your own insurer about the incident but this way you avoid paying out an excess and , by not claiming against your own insurance , save any hit on your NCD , although your renewal premium may still go up as this is unconnected to NCD .