Evie, I agree with you - you have a moral dilemma here. But from where I stand, that is all it is - a moral one - not a legal or even obligatory one. Look at it this way:-
Instead of fibro, you had developed bad endometriosis. You probably wouldn't want to share that problem, or even half a dozen other medical problems with your employer or other employees. I would keep this diagnosis of fibromyalgia to myself until such time as you knew yourself it was affecting your working life. Then you could be half hearted about your disclosure - tell them you are having a bit of muscle pain or discombobulated thinking at times or whatever. Give the symptoms not the full diagnosis, and let them figure it out themselves and maybe come to you and ask for a fuller version. You aren't telling lies - just protecting yourself from invasive questioning that at this stage doesn't concern them - or does it?
From my past experience, when I was working and before fibro was diagnosed, I had a mental breakdown with aphasia. My marvellous memory went and so did a lot of my technical abilities, and has never fully returned. I was the Lead Researcher and Head of a Research Unit, and was well known for my memory and without it I found it impossible to do the work I expected of myself. No one could give me the sack, but I didn't meet my own expectations any more, so I left after taking some time off to see if my memory and abilities returned. They didn't.
I obtained another position at another laboratory where less was expected of me, and eventually had to leave that also, as I couldn't eventually do that job either.
What I am trying to say here is, you will know when you can't do your job and so don't pre-empt the situation. Wait, and let the decision to leave or cut your time to when you really need that to happen, not before.
Can understand and empathise with you.

Likely good advice about disclosing with the union...I struggle with sharing the huge piece of my life of chronic pain etc with work scenarios/ situations as well. I'm a caregiver/ cna by trade. I don't like the idea of laying what could be considered " a burden" down to those I'm caring for. It's very easy for someone being cared for to want to assume the responsibility, deflect from self, the gamit. As well, I don't want any confusion about the reasons for sharing the information. I don't want to create doubt about competency simply because of misinformation, or preconceived notion about what I say, or the diagnosis itself. It's at least a part time job just doing research to accommodate an understanding about the disease. I wouldn't expect a client to assume that to have accurate info...
Now, if I where say, at Boeing, or another industry that required a different type of engagement with people, I would definitely share with the union and upper management as to help have support lined up. I can imagine being a teacher, HR would be supportive and noninvasive beyond absolute necessity.