Ive been through the exact same thing bro. glad you caught her. word to the wise, you can sue an individual, but making them pay up is an entirely different issue. You will win, no doubt about it, however you likely wont ever see a dime, or it will take forever to collect as was my case. Go after the insurance company. They have money. They will admit fault if you push hard enough. THEN sure her for any costs you incurred if you want to just to be a dick about it.
Fact is, if she is the kind of person who would hit and run, she likely does not have the common sence to have enough cash in the bank to pay for things like this... which is also likely why she ran in the first place. If she had cash and was self centered enough to do this, then her car would have been fixed by now and you would not have caught her. Pick your battles wisely and you will always win.
Hit me up on PM if you want to hear the rest of my story. Basically the courts can say youre right, but only an attorney can force her to pay... and they charge for that.