Have you had a sleep study or nap study done? Going straight into the dream state (REM phase of sleep) is the main problem of that. REM sleep brain waves are the closest to wakeful brain waves on the "sleep brain waves" spectrum. Deep sleep, which is where we actually get rest and our bodies restore themselves, emits waves the farthest from wakefulness. Another hallmark of narcolepsy is disrupted sleep patterns like you describe. If your brain doesn't reach deep sleep, even if you are sleeping, even if you get a full 8 hours, you won't be rested & you'll feel fatigued.