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Unfortunately, SSDI doesn't have to prove there is work for you. SSDI uses the Dictionary of Occupation (http://www.occupationalinfo.org/) to classify jobs. Personally, I can think of numerous jobs that meet the description mentioned.
It's more unfortunate that you were denied. My best advice is to search for a vocational expert of your own and get assessed. Just do a search there are numerous resources for you. Also contact any disability service in your area that could recommend someone.
The statistics are that 30.7% of all denied claims are "able to do other work." Another sad statistic is that 86% of all claims are denied at the 'reconsideration level' which is the first appeal.
When you are denied at the hearing level in front of an ALJ (administrative law judge) your second appeal, you can file a second application that includes aditional evidence of your inability to work. See SSDI-Help.com, Tips and TEchinques for instructions on to file a second claim.
There are a number of supplemental forms you and your doctors or mental health professionals can complete and submit as evidence. SSDI-Help.com has a listing of forms for printing you can use. In your case I would recommend: Adult Function Report, 3373-BK that you complete; Mental Residual Functional Capacity, 4734-SUP that a mental health professional completes and Physical Residual Functional Capacity, 4734-BK that a physican would complete. These are complicated forms so be thorough and patient. Get copies of all your medical records.
Good luck,
Trudi