Sleep Aide

I am going through a miserable cold.  The doctor prescribed for me some sleep aide medicine that was non-addictive.  I took it at night before I went to bed.  Not much happened for the first hour or two or so I thought.  But I found that in the middle of the night when I probably was most bothered by my cold, I was sleeping as well.  I had dreams filled with anxious events and moments.  I would wake in the late of the night, around 3ish and get up, cough and blow my nose and lay there in some meditation since it did not seem that I would go back to sleep.  Then I would sleep into the morning, waking up and going back to sleep.  The dreams in the early morning were very peaceful and happy.  They were the kind of dreams I would like to go back to whereas the ones from earlier in the night, I was glad they were only dreams.  I don't know that dope has anything to do with dreams or if middle of the night deep meditation affects dreams.  I only know I had this experience.  What do you know about this?