How do I know if the edition I have is the right one that I paid for?
Welcome to the forum!
The short answer is...you don't. Not by looking at your software...the only thing you can do is to go to your account on Logos and check your purchase history, it has a record of everything you've ever purchased from them.
Which one do you think you've got?
I assume you want to double check that you have the correct base package. Really, the only way to double check is to open your library and spot check resources.
Look on the comparison page (http://www.logos.com/comparison) for a resource that only your package (and above) would have, and check to see if it's in your library (Don't do this with interlinears though--they aren't listed separately in the library window).