In order to collect unemployment, you must have lost your job due to a lay off, reduction in hours, etc (i.e. you are not eligible if you were terminated for cause or if you quit). In addition you must be ready, willing and able to work and be actively looking for work -- therefore if the doctor is stating that you are disabled then bottom line you are not able to work and therefore you are not eligible for unemployment.
In terms of collecting disability -- it would depend on the definition of disability contained in your policy as to whether you are eligible for coverage and for how long. I suggest that you read your policy and/or call the agent or company for additional information and assistance in filing a claim if you are eligible.
I hope that your situation improves and wish you the best of luck.
Certified Insurance Counselor, Licensed Insurance Agent & Broker for over 29 years.