The at-fault party's insurance carrier is liable for the property damage to your vehicle, which is the cost of repairs.  If they are denying your claim for the problems that developed a month after the accident, obtain a written statement from the mechanic that these problems were caused by the accident.  If the insurance company continues to deny liability despite the written statement from the mechanic, file a lawsuit for negligence against the at-fault driver / registered owner (if the registered owner is someone other than the at-fault driver.  Name both the at-fault driver and registered owner as defendants in your lawsuit.