You have the right to hire or fire any attorney at any time. Depending on the fee agreement signed, your attorney may have a right to "lien" your file. This means your attorney may be able to keep your file and will likely be entitled to a portion of your settlement should you choose to switch attorneys. Practically speaking, often when a client switches attorneys the client's portion of the settlement remains unchanged, while the current and former attorney workout a spilt of the contingency fee. However, you should know, that switching attorneys may impede settlement if the two attorneys are unable to agree to a fee split. In rare situations, the settlement is deposited with the court and a judge decides the entitlement of each person.
Attorney Watkins is spot on in his analysis. You will want to make sure your attorney is still representing you. Many law offices will drop a case if there is a coverage issue, and they will send a letter to your last known address. There are many problems with this practice if the person has changes addresses or does not communicate via US mail.
I started practice as an insurance defense attorney and wrote many coverage opinions for insurers. Depending on the insurer or the insurance agreement with the defendant, there might be a coverage issue here since an unlicensed driver was driving another's car. When selecting an attorney, it is quite important to hire one that has experience in insurance law. These issues can arise and confuse some attorneys.
Some PI firms in Las Vegas that get their clients mainly by advertising hire non-lawyers to basically run the cases. In theory there is a supervising lawyer to keep the State Bar off their backs.
I think you should feel free to consult with a new lawyer to see about taking your case; if you have only been served by legal assistants I think the new lawyer can take over without worrying too much about a lien, although you should get the new lawyer to pay any lien from the old lawyer out of their fee.
That said, as another answer pointed out , there could be problems with your case such as insurance coverage issues.