What is occurring is not sleep paralysis, so what is it?

I've had 3 experiences within the past two months. In my dream, I was in a car and I noticed a UFO. The windows of the car cracked open slightly and the UFO got closer and brighter. As it got closer, I had more and more trouble breathing- like something was on my chest. As soon as my girlfriend woke me up, I was able to breathe again immediately. She also had had a nightmare that night. In my second dream, I was walking through the house and when I got to the living room, the television turned on by itself. As I watched it, I noticed a robed entity walking across the screen. Each time it ped, it got closer. I started screaming in my dream and shouting "f*ck you" at it. Again, my girlfriend woke me up because of my screaming. As soon as I was awake I was fine. I went to check on the kids and then went back to sleep. The most recent one occurred last night. I was laying with my daughter in bed and we were looking at pictures. We saw this one picture of an ordinary dark haired man in black dress pants, white shirt and a tie. However, it was evident that he was an apparition in the picture because you could see the background through him. At this point in my dream, an unseen entity tried to lift my daughter and take her away from me, but I was able to hold on. Again, he tried to take her away more forcefully, but I managed to keep hold. My girlfriend woke me up again and said that I was holding her rather tightly and I was whimpering. In all these dreams there was an overwhelming sense of evil. I have researched and tried to find out what it is with no success. The closest thing I have found is sleep paralysis, but it doesn't jive with the description. I would like to point out that my girlfriend has had instances where she was unable to breath, even after she has woken up. She says that it felt like suffocation. I would wake up and as soon as I touched her, she was fine.