You might research, 'LUCID DREAMING'.
The brain is a very intricate thing; it can act as-if it is a completely different person. It can be belligerent to you, frightened of you, it can retaliate against you. When one is starting to learn about their dreams, it is also possible that you were already having nightmares all night without waking-up... and now, you are seeing the nightmares that you were having.
It is highly possible that, sometimes, dreams might be coming from the 'other' side of our brain than our 'ego' side. Some call it the 'Subconscious', psychiatry might call it the 'ID', and it is also possible that different people use dreams in completely different ways from other people. Maybe for some people, dreaming is connected to their subconscious and with other people, that isn't true at all.
Myself, I am learning how to do LUCID dreaming; so I will look at it from that aspect, whereas you might not even know what that means.
When one starts to do LUCID dreaming, your dreams suddenly become vivid, sometimes. So vivid that they seem as real as what we call 'reality'. That's, probably, because your dreams are ALWAYS vivid. We just don't remember them at all, or we remember the last ten seconds of the dream just before one wakes-up. This aspect of dreaming is why you might not be AWARE that you were having nightmares; but, now that you are becoming more interested in your dreams (by logging REM periods, for example)... your brain cooperates by starting to show you what you were dreaming - and that turns-out to be 'You are experiencing nightmares when you dream'.
I would suggest that you start reading about LUCID dreaming. Why? Because when one learns to LUCID dream, one starts realizing that one can CONTROL their dreams, and if one becomes aware that they are dreaming inside a nightmare? Then it suddenly becomes understandable to the dreamer - because how can a dream hurt you? Thus, instead of running away, or thinking it will hurt you, you suddenly realize that a nightmare is just part of your own brain. It is an indicator that you are afraid of something.
Once a person becomes LUCID in their dream, they can do strange things... such as TALK to the creatures/things which seem to be attacking you. Oftentimes, they will TELL you what the problem is. And, oftentimes, that thing which chases you just dissipates. It stops by losing its power over you.
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There are many books on LUCID dreaming... but the scientist who studied it the most... the first one who outlined how one gets there and proved that it was a real thing (by getting the dreamer to move their eyes back-and-forth a certain number of times once they achieved LUCIDITY inside a dream) is called 'Stephen LaBerge'.
Order one of his books from Amazon (or used book on E-Bay) such as, "Exploring the World of Lucid Dreaming".
Basically, the concept is simple (and some people start to LUCID dream just by hearing that it is possible). The method consists of this:
1. Log your dreams until you can remember at least one dream per-night.
2. Notice what things that you tend to dream which are unique to the dream world (in my particular case it is seeing kids or being at a Boys and Girls Club because I used to work at one; but am now retired so never either see kids or work at a B & G Club). These are called 'Dream Signs'.
3. Use one of your dream signs during the daytime... in my case, "Every time I see a kid in the real world I ask 'Am I Dreaming' and do some sort of test in the real world such as poke my finger into my palm, which is an easy one... or look at one's watch and note what time it is. In a real dream, a finger oftentimes goes through your palm and a watch won't show you the same time every time you look at it. Others leap up into the air; because in a dream there is no gravity and you float; but it also looks weird in the real world to suddenly just leap up into the air every time you see a kid. It's called 'being nuts' in the real world when people do such things.
4. And, envision yourself becoming aware inside a dream. Also, before you go to sleep give affirmations to yourself that, "Tonight, when I dream, I will become lucid in my dream'. And, 'Tonight, I will remember all my dreams, vividly.'.
And, that's about it. I bought pens which light-up by clicking the pen out so I don't have to even get up to write down my dreams.
There are other aspects that can help you get Aware inside your dream which are laid-out in his books, as well, such as how to 're-enter' a dream, how to set timers to wake up every 90 minutes, then wait 20 minutes doing something, then going back to sleep with the intent to re-enter as an aware person into a dream - which is much harder to accomplish.
