When I got sick I wrestled with going on disability for a few months, but I applied anyway. A few months after I applied I started having seizures. When I went back to the doctor and told him about the seizures he said he could NEVER release me to go back to work. I was a truck driver and obviously I am not about to put the public at risk.
I hope you don't mind my being blunt, but screw what everybody else thinks! You are the most important person in your life and you need to take care of you!
Document everything! List all of your past jobs, list every doctor you've seen relating to your illness, and make a note of all of your symptoms. You can apply on line, but if you do, remember to print out a copy of your application because you will get more paperwork later asking the exact same questions so it makes it easier for the second application. It will take a few months (about 6 months in my case) to get a determination. If you are denied, appeal. If you are denied again, appeal again. Take it as far as it will go until you need a lawyer. When you are finally approved they will go back to the date of your first application so do it as soon as possible.
Good luck and I wish you the best! 
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