Will my payments raise if I move?

I am currently living in Virginia. I'm deaf and am on social security benefits. I recently stopped receiving SSI because now I'm receiving child AND disability benefits so I get about $730 a month. I plan to be on these benefits only until I find a better job. I've always dreamed of moving to southern California. I've heard that because the cost of living in CA is higher, your SSI checks will raise. I'm not on SSI but on social security benefits and I think they're the same thing since they all are government funds. So is it true I will get a raise if I move to CA to help pay the higher rent? Thanks in advance!