So I know that she got an errata to where she has a trait that says she can use Super Strength. When playing her at a tourney is there anything I need to show to prove that she has that errata and its not just me making things up? Or is it just a house rule?

The Players Guide would be a good place to start

Any players guide that has been released since the figure's release should work.
Go to heroclix.com, and they'll have a Player's Guide under the download sections.
There's also this, the updated preview for Power Girl with the correct Character Card.
Hope that helps!

Thanks guys. My JSA team just continues to get better