Trying to handle the UM side is a mistake, and you would want to retain a personal injury lawyer to go after that money, as they don't just hand it over to you like candy. The same lawyer can resolve your vehicle issues.
Why would your attorney lie to you about the offers from the insurance company? If your attorney, like most personal injury attorneys, works on a contingent fee basis, he/she would be interested in getting you the highest compensation possible and will not lie about the offers from the insurer. In addition, this information is really easy to verify.