Hi there,

I'm using Cool Edit Pro 2.1 for all my recordings. Cool Edit got bought out by Adobe a few years ago and now Cool Edit is called Adobe Audition, so I'm basically using the same program as you.
Now my amp has two speakers so the signal coming out of the amp is in stereo. If you are using an amp with just one speaker, it will be a mono signal, so what you are experiencing is normal and expected.

I'm not familiar with Adobe Audition, but in Cool Edit, there is an option to turn a track that's just on the left or right signal into a stereo or mono signal that comes out of both speakers. Try using the help to find the option.

Hope that helped...