I was convicted following a trial in federal court. Can I file an appeal?

Yes. If you pled not guilty, went to trial, and lost your case, you have an absolute right to file a direct appeal. If you were convicted in a federal court in Texas, you would appeal to the U.S. Court of Appeals for the Fifth Circuit. You can seek relief based on errors that occurred during the guilt-innocence phase of your trial or during the sentencing phase.