I could only think of 3 ways to counteract this:
1. Get more sleep
2. Get the same amount of sleep, but better quality (keyword: sleep hygiene)
3. Mind Control (observe your thoughts that make you feel anxious or sad and counter/question them with positive self-talk)
by the way: when I'm really sleep deprived for some days and then cancel a whole night of sleep, I get afraid of nearly everything (loud noises or what might happen in traffic). Somehow I think Sleep-Deprivation acts as an amplifier of all the fears, that are already there.