What can I do about a car accident and the damages to my car?

Since the other party has not contacted her insurance, you should file a claim with her insurance company for your property damage.  If it turns out that she does not have insurance, you can file a claim with your insurance company if you have uninsured motorist coverage.  If there is a police report, the police report of the accident should list the insurance information she provided.  The other party is clearly at fault since you were rear-ended.  If the other driver's insurance company denies liability, you can sue the other driver for negligence.  Your damages (the amount you are seeking to recover in your lawsuit) would be the cost of repairs to your vehicle.  Your damages should also include expenses such as a rental car.  You will need to mitigate (minimize) damages by selecting a repair shop whose repairs are comparable to others in the area.  You will also need to select a rental car whose rates are reasonable.  If you were to select the most expensive repair shop and/or an expensive rental car, you would have failed to mitigate damages and your damages would be reduced accordingly.  If the other driver's insurance company accepts liability, they should pay for a rental car for you.  They may have a maximum daily rate for rental car cost.  The collision damage waiver on the rental car is not included and the insurance company won't reimburse you for that coverage.