I always have nightmares, is that normal?

Nop, not normal (as someone that had always nightmares)
So, yeah, after some time of having nightmares one just doesn't care anymore, from my side I had to learn how to give a ending to the nightmare (that was not my "death") to have other dreams, but really depends if its the same nightmare or different ones, for me it was more easy since it was only one nightmare so I just had to go through trial and error until I gave a ending (escaping since I couldn't touch that thing or I would wake up instantly)