Unfortunately, this is pretty typical conduct for insurance companies – even though Social Security has found a person totally disabled, the private insurers try to find a way to avoid paying benefits.
If your LTD insurance was provided through your work, then it falls under the federal law governing employee benefits, called ERISA, and the insurance company should have told you in its denial letter how to appeal the denial. Usually that involves making an appeal directly to the insurance company, and only if it continues to deny the claim can you go to court. The appeal must be made within a specific time period, or you will lose your rights.
If you obtained your disability insurance from somewhere other than your employment, such as purchasing it directly from an insurance company, then ERISA may not apply and you would most likely be able to go to court and sue for breach of the insurance contract.
You should contact a lawyer right away, especially because of the time limits that may apply. To find a employment attorney who represents employees, rather, than employers, you might visit the National Employment Lawyers Association, at http://exchange.nela.org/findalawyer