Like many others, recently I have found I am unable to Add Media and Add Tags to my WordPress posts. The first thing I did was disable all of my plugins to make sure there wasn’t a conflict. In my cases there wasn’t, but its well worth trying this first. The next thing I did was switch my theme to the built in 2015 theme, and this fixed the problem. So I went to my normal theme creators web page and found that the theme had an update available, so I have downloaded and installed it this morning and everything is working fine again.
So in short, if you are having the same problem, try switching to another theme!