Actually, REM sleep is normal in all of us. It is the 5th stage of sleep and we (almost) all get there every night. REM sleep stands for Rapid Eye Movement sleep and the dreams associated with it are due to the high brain activation. REM sleep isn't discriminatory to nightmares, REM sleep brings about any sort of dream.

Actually, the more REM you get, the more well-rested you will be as its the deepest stage of sleep. If you are super exhausted, you will reach REM sleep faster.

I experienced nightmares and a lot of REM sleep when I was going through a lot of stress once: so I was exhausted and had a lot of negative thoughts on my mind which induced frequent nightmares.

Getting a lot of REM sleep is actually good haha the nightmares might have something to do with current events in your life.