Let insurance handle it. If anything tell her to use that 200 bucks for her deductible if you cant get it back from her, The insurance will usually setup a rental car if it has to go to the shop. The medical claim is probably nothin to worry about, claiming injury and having visible injury is a huge difference. Also the estimator for the insurance will do the inspection and be semi aware of whats possible at certain speeds.
Not sure of the legality of the note and pay out though good luck. Also if you happen to get questioned about the accident and they ask " how long did you have to respond to the vehicle stopping" Don't tell them too short of a time cuss it'll just make it look like its entirely your fault. Even though in rear end collision the person in back is just about aways the guilty one