do teachers not have the same rights to post on social media as everyone else?

Yes, as a general rule teachers have the same rights to post on social media as any other employee; they also have the same restrictions. The fact is that an employer may prohibit social networking on work time or posting anything negative about the company any time, etc. So, if your employor had a social networking policy and you violated it, that could be grounds for termination (you'll need to check). That having been said, if your treatment constituted some form of legal discrimination or violated the terms of a union agreement or employment contract, tha would be illegal. Otherwise, as an "at will" employee, your employer can set the conditions of work much as it sees fit or deems appropriate. That having been said, while an employer has the right to take some form of action against an employee regarding prohibited uses of social media, many states have laws which prohibit employers from disciplining employees from certain conduct outside of the workplace and many are written broadly enough to cover online activity. Additionally, a social networking policy that is too restrictive may be a violation of the National Labor Relations Act (although such is not appear to be the case here; that has to do with discussions of workplace conditions). At this point, you can consult directly with a local employment law attorney who can best advise you of your rights here.