How to retain image quality

I can't figure out what I'm doing wrong.  I edit a picture and it looks great.  I drag the layer from one file to another file and the image deteriorates drastically.  I've tried saving the files as .psd and .jpeg with the same result.  I flatten the image before I drag it with same result.  I can't combine images without losing quality.  None of the tutorial videos seem to have this problem.  Is the problem my iPhone?  The image looks great when I download it. I'm in Elements 15.