How much anyone else received has absolutely nothing to do with how much you will get. The amount you receive is based on your work record (if any) and your onset date as determined by Social Security. And backpay can take anywhere from a couple days to many months. A lot depends on the worker(s) handling your case and if you have submitted everything on your end.

Waiting for your letter and your backpay is part of the process. You just have to deal with it!