If the tire chains are are installed and fitted properly, you can damage a lot of stuff and make the car very unsafe in the process. From what you have described, it would appear at least one or more wheel speed sensors are damaged. That is why the ABS and traction control lights are on. You may have also damaged some brake lines too. You need to pull all the wheels and check for any physical damage to any wires, brake lines, brake hoses, and struts. At least that is a starting point.