It seems that your issue boils down to your suffering from work-related stress, and that this stress is increased due to the fact that you are in a profession where you are supposed to be able to understand and heal the very illness of which you complain. Your fear is that by making the true complaint, your employer will decide that you are not competent to practice for the school district, and so you may be terminated from employment.
I'm not a mental health professional, but it seems to me that you are placing far too much importance on your profession somehow making you immune from the same problems which befall your clients. I can certainly tell you that attorneys get into legal troubles all the time, and they are frequently no better at extricating themselves without legal representation as any layperson -- because when a person suffers a problem -- any problem -- they lose objectivity and they cannot heal themselves without assistance.
Were I representing you, I would probably recommend that you file an FMLA request and take some time off to collect yourself (and, possibly to apply for some other employment, in a less stressful environment, while you are recovering).
The one thing that I would not recommend would be a disability discrimination claim. Requesting reasonable accommodations for your disability, in my view, would fail, because, as you have pointed out, you are a mental health professional, and no reasonable accommodation for stress will permit you to perform the essential functions of your job. And, that means that the employer can terminate you without violating the Americans with Disabilities Act. So, while the ADA reasonable accommodations avenue might be the best solution for someone who is not a psychologist with stress-related injuries, it may produce the exact defense that the employer needs to terminate you, precisely because you are a psychologist.
The point here is that if you take 12 weeks off to get your head straight, you can come back to work and start over fresh (unless you find other employment in the interim). The fact that you were having difficulties that led to your FMLA request would be irrelevant on your return, because you won't be requesting reasonable accommodations for a disability. Instead, you just needed some rest, and when you return to work, you're fit for duty and ready to go again.
Yes, it will cost you some lost income, but sometimes money must take a back seat to health. And, you can probably get short term disability while you're taking the time off, so you won't be coming completely out of pocket for your self-imposed sabbatical.
Hope this helps.
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