I have tested the same at my end and its working fine. I am using Photoshop CC on Windows 10 platform. You may try and reset the Photoshop preferences back to defaults and check if that helps.
Refer: Preferences in Photoshop
I think part of my question got cut off. I did reset the the preferences and that didn't help. I was able to drag and drop one of the loaded photos onto the other one and it would automatically load a layer. Now, when I do that, nothing happens. I use the move arrow and unlock the photos and still no added layer.
Lets see if you are doing exactly the same as here.
Use the move tool and click on in image one
Drag it to the tab of image 2 and keep holding
Wait until the tab changes and the image changes to image 2 (still keep holding)
Drag down onto the canvas of image two and release - the new layer appears
(press and hold shift before releasing if you want the new image layer to align to the canvas)