Is it normal to have a phobia of nightmares?

It's normal, especially if you use drugs. If you don't, it depends on what there is happening in your dreams. Don't worry if you don't get any sleep in even more days, eventually you will fall asleep and then you have most scariest nightmares ever. :-)

By definition, a nightmare is a scary dream. By definition, a thing you find scary is something that scares you. A phobia is a thing that you have a fear of (a thing that scares you).

So yes. Your question is somewhat redundant.

had the same when I was on cold turkey

Sure, all it is is a fear of fear. What is it you usually dream of? What are you watching or listening to before you sleep?

Yeah, its normal to have fears of nightimares, but having them all the time I'm not so sure. Btw the song Enter Sandman by Metallica is about fear of nightmares (sorry, music nerd =/)

There are times when I have more nightmares and it makes me scared to fall asleep =/ I always think this guy who tried to kill me is gonna get me next time.
If it's really badly effecting the amount of sleep you're getting you might wanna talk to someone who can help. x

You should look up what causes nightmares because certain foods do that such as spicy food and fast food and sleeping right after eating as well as if you aren't getting enough oxygen during sleep ie if your blanket is over your head.

I know when I have a bad dream I am always afraid to go back to sleep but not any other time. I think this is kinda normal.