This is very case-specific so you should talk with a lawyer offline who can review those specifics and advise accordingly. Best of luck
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It would be unlawful for your employer to fire you for requesting reasonable accommodation for your carpal tunnel condition or to fire you for being on FMLA. See what accommodations HR can give you while you recover. Also, if you were injured on the job you should apply for workers compensation and an employer cannot fire you for seeking workers compensation.
This is not intended to be legal advice, but is only for general information. Cantact an attorney in your area for legal advice.
Please call a lawyer near you in Houston. It sounds like you have a good case.
Attorney David Snyder is licensed to practice in the State of New York where he operates the Snyder Law Firm located at 6876 Buckley Rd., Liverpool, NY with a web address of www.snyderlf.com and www.syracuseworkerscomp.com. Mr. Snyder’s answers are intended to assist legal consumers in obtaining the most accurate information possible and to find the most appropriate lawyer when necessary. In no way can any of his answers be construed as legal advice without being retained and having all relevant information available to him.
Is your medical provider telling you that your job is a producing cause of your CTS? If so I would strongly advise that you file a workers compensation claim.
It is odd that they are asking you to dictate the accommodation. Generally the employer insists on their right to dictate the accommodation. In addition to contacting a lawyer, as others have suggested, I would suggest making it clear that you are open to their suggested temporary accommodations so long as they accommodate your medical needs.