Dear Customer, I am sorry to learn of this situation. You really need a new attorney (preferably a legal malpractice attorney) to take a look at your actual documents to help you identify what exactly the status of your case is. (If you didn't sign a settlement with the City, your case should not have been dismissed, therefore there is no need to refile - however, if you did sign a settlement agreement, you cannot refile the same case a second time, regardless of the circumstances of the settlement).
A local attorney can also help you take a look at the lawsuit filed against you by the City and see if that would be precluded by the settlement agreement, and what, if anything, can be done to dispose of that quickly without having to go through another course of litigation.
Legal malpractice cases are based almost entirely on expert testimony. You must not only find an attorney to act as an expert witness regarding the standard of care for your prior lawyer (to prove the "negligence" elements of the case), but also an attorney expert (and potentially other experts) to testify regarding the underlying claim (you must prove that absent the attorney's malpractice you would have achieved a better result - often termed "the case within the case").
Due to the complexity of these claims, I highly recommend that you retain a legal malpractice plaintiff's lawyer (also called trial attorneys). Fortunately the majority of these attorneys will provide you with a free consultation, and many will represent you on a contingency basis (they will advance the costs of litigation and legal services in exchange for a portion of your successful settlement or judgment).
You can find local attorneys using the State and Local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).