We were prohibited from using any social networking sites from our work computers. You'd need to check your employers' policy on the use of social networks and publication of pictures taken on school premises.
Usually work places are very strict about using the computers for anything other than work, even screensavers were frowned on where I worked. I'm told it is possible to introduce a virus into their computer system by using unathorised sites etc.
It sounds like it does make a difference. Each employer is free to make their own decision and if yours says no to posting photos of work in work time then apologise and move on.
If you continue to argue against them they are likely to take it further.