When you face criminal charges, you will either go to a state court or a federal court. It depends on the criminal charges as to which court will hear your case. If you face federal charges, your case will involve a federal prosecutor and take place in federal court. You must go through the federal court system for anything involving your case, which includes an appeal.
According to the United States Department of Justice, you may appeal a criminal conviction if you have been wrongfully convicted. However, when appealing a case, the Court of Appeals does not conduct a new trial. Instead, you must prove that there was a mistake or issue in your original trial that makes it invalid. Appeals require that you or your counsel successfully argue that a mistake of law was made by the District Court which entitles you to relief on appeal.
If you want to appeal your case, you will have to do so through the Court of Appeals. If you do not agree with the decision of the appeals court, your only other option is to take your case to the U.S. Supreme Court. The Supreme Court only hears a small fraction of cases, and the court, typically, limits itself to hearing cases which have broad implications. The Supreme Court does not have an obligation to hear all appeals.
An appeal to the Court of Appeals may end with the court sending your case back to the lower court for a new trial. The Court may also reverse the ruling of a lower court or change your sentence. If the court upholds the lower court’s ruling, it means that it agrees with the lower court, and nothing about your case or sentence will change.