I can't think of any exceptions to the rule that you cannot get a writ of habeas corpus in a Texas state appellate court until you have first sought one in a Texas state trial court. Cf. Ex parte Young, 418 S.W.2d 824 (Tex. Crim. App. 1967) (orig. proceeding). An appellate court does not have the capacity to make a trial record, so if you want habeas relief you have to start where a record can be made: your trial court. And remember the AEDPA clock is running from the time your trial judgment is final (not counting the times that appeals toll the finality of the judgment), and the total time you have for all your habeases is one year.
So don't start in the appellate court, bubele.