Here's info on SSDI and SSI:
http://ssa-custhelp.ssa.gov/app/ans...social-security-disability-and-ssi-disability
I receive SSI and have for many years. Its not much but does pay rent, bills and comes with free health care. You can apply on your own or with a lawyer. Having a doctor that backs you up is always a good idea. Luckily my lawyer works with a doctor.
Social Security will ask you about your rent, bills, who you live with (if you have a significant other say they are you're roommate and nothing more, everything is half and half, not until you're married), health (think of your worst possible days and don't say that sometimes you're fine or can manage), hospitalizations etc. Most people are denied their first time applying (I heard of a guy who had no arms who was denied his first time applying, its just their policy to weed out those who really aren't in need) but you must file for an appeal. Having a lawyer makes the process easier and faster. They take a percentage of what you're awarded in the end (you don't have to pay them unless they win your case and when you do win its usually a large sum because they go by when you first applied to when you were accepted so there's really no issue when having to pay off your lawyer if you're already working).
Having SSI helped me finish school otherwise I probably would have never finished college and grad school cause that and a job was just too much back then.