No, the amount you receive for SSDI/SSI will not increase.

Look for a HUD (I take it that you're in the USA) office and go fill out paperwork for subsidized housing in your area. It will be a shorter wait than getting onto the section 8 housing waiting list. Check for that too. Google 'section 8 housing (your city)' and find out the status of the waiting list.

Rent will generally run about 30% of your income, perhaps a bit less.

hth