After testing my hosting server I channged my AddThis code and deleted the previous profile setting up the new one for the active domain after registration. But the new connection didn't work. It seems illogical to me that I should possible keep the old connection with a new domain. I think I should set up the account at ShareThis and find better luck there - they are also good, I suppose?
By the way, while selecting Facebook for WP plugin, should I NOT include FB in ShareThis list?