I am very sorry to learn of your situation. I have also read your other posts, and saw that you posted a similar question earlier today.
Unfortunately, if your lawyer did not file before the appellate date, your attorney has created an insurmountable error. By missing the appellate deadline he effectively terminated your ability to attack the Board of Nursing decision. There is nothing the courts will do at this point.
You do however have the basic facts to put together a legal malpractice claim against him. Missing a deadline is one of the most common errors leading to legal malpractice. While this will not get you your nursing license back, it will however provide you with an avenue for financial compensation for his negligence.
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).
Again, I am very sorry to learn of your situation, and I do wish I had different information or a different answer for you. But I do want to provide you with accurate and correct information so that you can move forward productively.