What do you want to do?
It seems you might know Corel really well, what's that going to hurt?
How well do you know Illustrator? If you have 13 years of Corel experience, then that is probably not going to go anywhere. If you plan on moving up the design food chain, then look at the software that is required at certain shops or design firms and learn that. If you plan on interviewing for a job right now, then you might be at a slight disadvantage if they require more than Corel, you just dazzle them with your portfolio and explain that you can learn any software they require.
One thing you do not want to do. Whatever job you interview for or get, learn the software and don't carry on about this software is better than that software... that gets old real quick.