Can I be covered by both SSI & SSD?

I have become disabled slowly over the past 10yrs due to a chronic illness. I was advised to apply for both Disability and SSI when it became apparent that I was no longer able to work. I stopped working March 24th of this year and was terminated by my employer on May 2nd. I have had zero income since my last paycheck in April and a pay out from my 403b in May that I used for rent. My daughter has been paying my rent and copays for my meds. I am getting food stamps and General Assistance Medical Program for insurance. I got a letter today saying that I was medically approved for SSI and that I had to make an appointment to see a worker to go over some paperwork before they can start sending me checks.

Well after searching this website it appears that SSI would pay $637/mo and Disability (according to the yearly statement we are sent), I would get around $1,100. SSI wouldn't even cover my rent, let alone utilities.