We assume your employer must be the carrier of the coverage, since Texas certainly doesn't have any type of state program, and Social Security disability is not what we are talking about here as it is not short term disability.
Who administers this program for your work place? If it is self administered by the company, this is unusual, as most companies have some third party (like Afflac) handle the short term disability. So the first question is, who is refusing to deal with this claim? Is it your employer, who is refusing to send it in to their carrier, or is it the carrier who has received the information about the claim and is refusing to pay on it?
In any case, it is your responsibility to determine who to appeal this decision to, and how to put it through the system. Incidentally, premiums for employee disability insurance through a person's work may be taken from employee's paychecks, but it still goes into a general pool, it is not placed into a separate account for you specifically, in other words, "I paid this in for myself, so I should be able to get it out!" Unless it is a private disability insurance held by you for yourself, it's not specific to you.
But anyhow, the company you work for will be who you are dealing with, at least at first, and will probably be referring you to a carrier of some type where there will be an appeal or review of some type before they just say "NO!"