You can still make an insurance claim. Unless the old lady who hit you is really dishonest probably no one will dispute you. First, call the police station and try reporting it even if they say it's too late. Not everyone carries a cell phone, so it might have been impossible for you to call from the scene of the accident.
Then try to call the old lady and see if you can get her policy number and license plate number. Even if you can't, you can still do the following:
1) Call the old lady's insurance company and report the accident even if you don't have all the information. It may have been too dangerous at the scene of the accident for you to collect all the information anyway. They will contact her, and unless she denies it you shouldn't have a problem.
Don't wait for her insurance company to get back to you.
2) Go to an auto body shop and get a free written estimate for the repair costs. Places with a special computer system for doing estimates are the best. Submit the estimate to the old lady's insurance company by fax or certified mail. By law, the insurance company has a certain amount of time to address your claim. The laws vary by state. They might want to look at your car themselves or send you to a different body shop. In California the "victim" gets to choose the shop.
As long as her insurance company acknowledges your claim, you should be able to get your car fixed, but you might have to be patient and wait a while. If you have any problems, check with your state insurance commission.