A probation before judgment is not a sentence, but a legal term that means that you've been placed on probation instead of being sentenced. The PBJ does not close the case. Depending on the type of charge, you may be able to expunge it after the end of your probation, and as long as you don't have other pending charges.
Probation Before Judgment is a disposition which means the judge has stricken the conviction and stayed judgment. Unsupervised probation simply means you do not have to report to an agent. You may still have conditions though such as "obey all laws." You should check your paperwork from court. A disposition of Probation Before Judgment is often eligible for expungement after three years. There are some exceptions.
The conviction was stricken under the Criminal Procedure Article 6-220 which means that there is no conviction for the purpose of any disqualification or disability imposed by law because of conviction of a crime. You do not have a conviction so there is nothing to appeal. However, the case remains in the system. Usually in criminal cases a period of probation is imposed and if you violate the probation you end up back in front of the sentencing Judge who can send you to jail and reimpose the conviction. A PBJ may be expunged three years after the case is closed or the period of probation is over if you are not on probation for a new case, have no new cases pending and have not received any new convictions, or new charges in those three years.