Have you considered utilizing Voc Rehab Counseling? They will provide testing, including medical, and help you find a job which may include government jobs that you can do from home.

Issues such as your come up when someone is simultaneously applying for UE and SSDI, and state rules vary widely. When in doubt go into your UE office and discuss your situation. It would seem to me that you are able to work with accommodations, and that you may qualify as eligible for jobs that are given first priority to disabled workers.