Can I recover even if the motorist never hit me, but caused me to have an accident?

Yes, you can make a recovery even if a motorist never hit you but did cause you to suffer an injury. For example, if a car was negligent in the way that it was driving, let's say that the driver was texting while driving. They swerved into your lane, and you had to veer off the side of the road. Even if there was no impact, you have a claim against that driver for their negligent driving that caused you to veer off the side of the road.