While I don't think every casual FB or google search is a big deal, this seems to be something that's really bothering you, so it does seem like you're better off telling him. You can't predict his reaction, of course--he might be angry as you say, but he might not. But if the therapy is currently at a standstill, maybe getting this on the table would move things forward in a useful way.

In addition, it would probably be useful for him to know what kind of information about him is available. He might want to ask his girlfriend not to post that stuff publicly. I know I wouldn't want my love life out there for anyone to read.