you will need to learn the Adobe products, plain and simple.
There is no substitute in the pro world, no way could you "convince" a serious employer that Corel would be ok.
Some concepts and techniques you will not have to learn from the ground up, since you have some foundation with the Corel products, just not all of them.
I wouldn't say you screwed yourself by learning the Corel stuff first, but doesn't mean you can skip the nitty gritty of the Adobe products.
It's kinda like saying, I know Adobe InDesign so I dont need to learn QuarkXPress. when in truth you need both.
Working with printing press requirements is where Adobe is king.
My advice, start with downloading the 30 day adobe demo's one at a time and learn the basics and work your way up.
Either spend a few bucks for »www.lynda.com
or college courses in graphic design.
lynda.com provides a 7 day free trial btw.