Should I hire a lawyer for a car accident in which I was sued by the other driver, but not at fault? Or will my insurance use their lawyer?

Your insurance company should assume the responsibility in determining who was at fault based upon the police reports from the scene of the accident. Under most circumstances, you provided your insurance company with the right to represent you in the event of a claim and they typically provide a lawyer to do so but remember, they represent the insurance company and although the insurance company is insuring you, I'd be very careful in making assumptions in your favor. I would begin by contacting the agent and following up with a letter requesting confirmation that you will be represented by the insurance company. If there's any confusion or delays, and you are definitely not at fault, I would attempt to find an attorney who be willing take your case on on a contingency basis rather than a fee. This will tell you just how good a case you have before you have to make any final decisions. Hope this helps and good luck