After jan's boyfriend broke up with her, she posted unflattering pictures of him on her facebook page and wrote about how he was a terrible boyfriend, calling him a liar and a cheater. jan's actions are protected by the first amendment to the constitution.

This is true.
Jan's actions are indeed protected by the First Amendment to the Constitution, which protects free speech. Jan felt betrayed and hurt by her boyfriend and she didn't do anything illegal by posting unflattering photos and writing bad things about him. What she did is morally and ethically wrong, but not illegal.