There are low income options that cost one-third of your income like stated above. You can get a list of these types of housing options from your state's housing/human development department. Also I have seen them listed in the classifieds in the newspaper.
You also would qualify for low-income assistance with energy costs for electric/heat and food stamps.
Do you have a case worker for the recent upgrade in your SSA benefits? If you contact someone from the letter you got, they should be able to help you with a list of housing resources.
I have some experience in applying for this type of low income/disability housing. It's not section 8 housing and it's not considered "welfare". I do not have any social security benefits. I just needed something with my Dx so I'd qualify as having a disability.