rear end cause mechanical damage?

[97Hyundai]

A lady rear ended me the a few weeks ago at about 15 mph, and my 97 hyundai elantra starting shaking and vibrating everytime i would stop. It started off as small vibrations and got worse and worse, until about a week later, I was driving and the steering wheel locked up and the dash lights came on and the thermometer went pass the H. I immediately pulled over and turned it off. To make a long story short, her insurance people who are handling this, are saying that they dont are not going to pay for it, because "you can not get mechanical, internal damage from a rear end collision." But my car was running fine, before this. If you know any information, please send to my email or respond on here. Thank You.