Well... I don't really know anything about this in particular. But it makes sense to me to discuss this with your doctor. You may or may not have narcolepsy. But that's not the only thing that might be going on here I wouldn't think.

I recall reading an article in our local newspaper a while that that talked about the importance of getting down into the deeper levels of sleep because this is where the body heals itself. So perhaps there is something going on with you that is preventing you from reaching those deeper levels of sleep. Thus, no matter how much you sleep, you're still tired. I've pretty-much always been tired too. In my case, I've always just presumed it was the result of the load of anxiety I've always carried around. Anyway... good luck talking with your doctor!