Have you looked for low income housing in the area where your school is? Since you are on SSDI, you are considered to have a "disability" and could get yourself on a waiting list if that type of housing does exist.
As far as food stamps, I won a case in my state with an administrative judge to allow the cost of food expenses related to CF (for those who have digestive issues) to be an ALLOWABLE medical deduction-they were saying it was a "special diet" and not allowing it. But we won and could use the food expenses for mark's CF as a medical deduction from income, plus a deduction for our rent (NOT subject to a limitation IF someone in the house has a disability as you do), so we qualified for food stamps for a while that way.
Do you get more or less than the $623 right now? I ask only because the way you worded it makes it sound like you would be recieving LESS if you moved out than you get now, and that just doesn't seem right. However, if you are currently recieving less than $623 while living with your parents, please disregard.
Have you filled out a FASFA? (Federal application for student financial aid). That can help you get scholarships and grants. For instance, in the state of WA we have the WA state need grant, in addition to the pell grant which is federal, and a few other grants that the school choose to give out. By filling out the FASFA, the school can figure ot a cost of attendance for you and figure out how much you/your family can contribute. Then you can ask for a re-consideration of budget amount because of your CF and inability to work AND attend school, AND a reconsideration of expected family contribution if you parents aren't going to assist at all.
You can also apply for scholarships. The Elizabeth Nash Foundation is one for people with CF. The Boomer Esiason Foundation has scholarships for people with CF, and sometimes your school also has scholarships available to give out as well.
Good luck!