Does a petition for writ of mandamus filed in the Supreme have to mirror the exact one that was filed in the court of appeals?

First of all, you should not be seeking mandamus relief without an experienced appellate attorney representing you. However, since you've already filed a mandamus in the court of appeals and if you continue to represent yourself in filing mandamus with the Supreme Court of Texas, I would suggest that you should only have 3 grounds for seeking mandamus relief. The more grounds you have, the more likely the appeals court is going to ignore your good grounds if they are outnumbered by marginal or meritless grounds. Your question correctly suggests that the Supreme Court of Texas will not want to consider grounds not raised in the court of appeals, and those grounds would probably be rejected since you did not present them to that appellate court first. I also suggest you call the Texas Supreme Court clerk's office and see if you would qualify for help drafting a mandamus petition through their pro bono attorney program. Good luck.