Can't get a nursing job

Earlier this year I did something stupid. After a 13 hour shift and taking sleepy meds I was on a socail network site and I mentioned a doctor's name instead of an initial. My boss saw it and fired me the next day. There's a strict policy about social networking. This was several months ago. I've been a nurse for a very long time 20+ years and still I can't find a job. I get calls from travel companies but at this point I can't do that and live in a state that doesn't have many travel positions. I need some advice on how to say what I did. Most applications ask if you've ever been termionated and then want you to explain why if it did happen. I've put that it was a mistake, that nothing malicious was intended, that I truly respect the doctor that I mentioned till I'm blue in the face. Anyone have advice?
not much to be done now. Take it as a lesson learned in social media separate personal from business, never friend anyone at work, if do set up specific access rights, i personally dont' friend em answer is sorry its for family and close friends only, use privacy settings, and also do not talk about work on social media aka facebook. always omit names, where you work, situation specifics aka nothing that you can use to ID someone "Ex: pt male 57 with mole on left cheek, tattoo on left arm of mermaid with barbed tale. Recite your story however you want to spin it until you no longer get flusterd, embarassed as you want to answer the question as if it was any other question. Anyways good luck .. and ya the job market is very tight so 20 year just means expensive according to employer as they ahve to compensate you for experience. Keep looking you'll find something.
So very sorry you're going through this. The only things I can think of are to be truthful, when inquired, but don't stumble over the why's and how's of the situation that resulted in the termination (it's in the past now, remember to K.I.S.S.) and to consider applying to smaller companies. Smaller places tend to have less applicants and less bureaucracy than the big corporate giants of healthcare. Dealing with social media use by employees is still a very new obstacle businesses are having to deal with in a professional, lawful manner. In a sense, everyone involved is still learning. Best wishes and this too shall pass.