I have had dreams where I go back in time and avoid saying something embarrassing, or go down a different path when making important choices in my life, but none that seemed so realistic as you described. I have dreamed of what my life would be like if I never lived in Korea, and that dream lasted quite a while and I have dreamed of similar things many times, but I don't think I have changed anything as life-changing as saving a loved one. Not that I really could, the family members I have that died were well on their way and nothing really could be done. I suppose I could make the last few years of my grandmother's life better; I hear she was treated poorly at the care center before she died.

I have a friend that I worked a bit with in Korea who used to get really deep into meditation, hypnosis, and lucid dreaming. He had a pretty difficult life, got in trouble sometimes and had seen some really bad stuff, and he had created an alternate reality where he was happy. Eventually he said he had to stop because he liked that reality more than this one, and he realized he didn't want to leave anymore. I don't know what inspired him to leave his world altogether, but now he is pretty happy, lives a good and safe life with lots of friends.

Something that this makes me think about, though: does it make it any less of a reality if these dreams come from you, from some sort of cosmic link between worlds, or divine intervention? I would say that even if the dream was just a dream created in your mind with no outside help it is still a reality. So yes, I think you experienced a changing of past events and an alternate reality.