Based on the facts you provided, as I understand them, you would be found "at fault" or primarily at fault for the accident, and therefore would be liable to pay for any damages that are the proximate result of that accident. In most instances that would be the amount necessary to cover the actual reasonable costs to repair her car to the way it was before the accident (and possibly something for loss of use). Your NOT responsible to pay to have the car restored to brand new condition. (BTW to the extent that she may have been partially at fault, say 10%, her recovery would be for 90% of the damages, as her recovery would be reduced to the extent of her contributory negligence in most states.)
If she had collision insurance and filed a claim with her insurance company, her company would have paid her or the auto body shop the cost to repair the car less the deductible and then it (and its lawyers) would seek to come after you. If she did not have collision coverage and you can't work it out between you her only option would be to sue you in a local court.
Unless she can bring her suit in a small claims court, that could be a daunting challenge, and she might need a lawyer unless she can get it into a small claims court. If she does sue you, you could default (and she'd eventually get a judgment against you which she'd have to collect -- not always an easy task) or you could deny liability and defend yourself either alone or through an attorney. You (or the attorney on your behalf) could deny liability, deny that the damages were as great as she claimed, and/or claim she was at at least partially at fault. If the matter were nt settled it would eventually get to court where a judge would decide at trial. At trial the burden is on her to prove both that you were at fault and what the damages were, which often would require her to produce a mechanic or a certified paid bill.
Fortunately for you, at least at this point, she is only claiming property damage to her vehicle. However, if she hires a lawyer all of a sudden she might also assert a claim for some personal injury (that sprain she might claim she got after the accident, or some recurrent headaches) which could complicate matters and increase her potential claim and your potential liability. (Of course if the judge senses she is lying about the personal injury it would somewhat sabotage her property damage claim as well.)
It seems to me that you have some negotiating power and to the extent she is acting unreasonably, that may play out to your advantage in the end, as few lawyers would want to take her case on and (except here on FreeAdvice.com) lawyers expect to be paid for their work, and that would come out of her eventual recovery.
I'm not commenting about whether or not your own insurance would be liable to defend you and/or pay the claim as I would need far more facts and to read the policy. And that I don't do for free.