Congrats on starting the commute. I think that 13 miles in 65 minutes is pretty fast when starting out!

I second the pannier and rack idea having that weight on the back must get uncomfortable. I think that racks and panniers are very versatile and can be loaded with more.

Also I think being a bike commutee with panniers you will look right in place. Soon enough you will think how foolish all the drivers look.