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

Can I recover?

It depends.

If the other motorist was at fault, if they were negligent, if they did something wrong, then the general answer to that question is “yes.”

Problems? You’ve got to be able to find them if they took off and left the scene. Then, that can create some issues, but generally speaking, yes, even if the other motorist doesn’t hit you, you can still file a claim for their negligence.