Does TJC report to the board?

HHS Office of Civil Rights is responsible for enforcing HIPAA.  I have no idea what TJC would have to do with it. Your former employer sounds less than stellar.

It's a good idea to review HIPAA in general if you don't have a good understanding of it. It's also possible that what you actually violated was a "privacy practice" or one of your institution's policies.

I've heard of people being terminated for various minor mistakes or for doing practices that were very common in their institution until someone decided to bring the hammer down on a certain person or situation; we've had posts similar to that here before.

Seems like for now there isn't much for you to do other than focus on getting another job.

No. The Joint Commission would not report a violation to the Board of Nursing. They would defer to the facility to make the reporting.